Equation Solver
Solve linear and quadratic equations with detailed steps
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Equation Formulas
Linear: ax+b=0 → x=-b/a
Linear equations are solved by isolating x. Quadratic equations require computing the discriminant first.
⚠ Note: a=0 reduces to linear. Δ<0 means no real solutions (complex conjugate roots).
What is Equation Solving?
Equation solving finds unknown variable values that satisfy the equation — a core algebra skill.
Transposition
Same operation on both sides preserves equality — the core principle for solving linear equations.
Vieta\'s Formulas
x₁+x₂=-b/a, x₁·x₂=c/a. Know root relationships without solving.
Completing Square
Rewrite as (x+p)²=q and solve. This method underlies the quadratic formula derivation.
Quadratic Formula
x=(-b±√(b²-4ac))/2a — the universal formula for all quadratic equations.
💡 Example: Solve 2x²-5x+2=0. Δ=25-16=9>0, x₁=(5+3)/4=2, x₂=(5-3)/4=0.5. Verify: 2×2²-5×2+2=0 ✓
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FAQs about Equation Solving
How to solve a linear equation?▼
ax+b=0 → x=-b/a. Move constant to right, divide by coefficient. Example: 3x+6=0 → x=-2.
Quadratic formula?▼
x=(-b±√Δ)/2a, Δ=b²-4ac. Δ>0: two distinct real roots; Δ=0: repeated root; Δ<0: no real roots.
What does Δ mean?▼
Discriminant Δ=b²-4ac determines root nature. >0 two real, =0 repeated, <0 complex conjugate pair.
What is Vieta\'s formula?▼
x₁+x₂=-b/a and x₁x₂=c/a for ax²+bx+c=0. Connects root sum and product to coefficients.
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