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(x+15)(x-12)=180
We move all terms to the left:
(x+15)(x-12)-(180)=0
We multiply parentheses ..
(+x^2-12x+15x-180)-180=0
We get rid of parentheses
x^2-12x+15x-180-180=0
We add all the numbers together, and all the variables
x^2+3x-360=0
a = 1; b = 3; c = -360;
Δ = b2-4ac
Δ = 32-4·1·(-360)
Δ = 1449
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{161}}{2*1}=\frac{-3-3\sqrt{161}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{161}}{2*1}=\frac{-3+3\sqrt{161}}{2} $
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