(x-7)(x+12)=66

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Solution for (x-7)(x+12)=66 equation:



(x-7)(x+12)=66
We move all terms to the left:
(x-7)(x+12)-(66)=0
We multiply parentheses ..
(+x^2+12x-7x-84)-66=0
We get rid of parentheses
x^2+12x-7x-84-66=0
We add all the numbers together, and all the variables
x^2+5x-150=0
a = 1; b = 5; c = -150;
Δ = b2-4ac
Δ = 52-4·1·(-150)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*1}=\frac{-30}{2} =-15 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*1}=\frac{20}{2} =10 $

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