x2-5x-56=-2x-2

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Solution for x2-5x-56=-2x-2 equation:



x2-5x-56=-2x-2
We move all terms to the left:
x2-5x-56-(-2x-2)=0
We add all the numbers together, and all the variables
x^2-5x-(-2x-2)-56=0
We get rid of parentheses
x^2-5x+2x+2-56=0
We add all the numbers together, and all the variables
x^2-3x-54=0
a = 1; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*1}=\frac{-12}{2} =-6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*1}=\frac{18}{2} =9 $

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