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(x+12)(5x-24)=180
We move all terms to the left:
(x+12)(5x-24)-(180)=0
We multiply parentheses ..
(+5x^2-24x+60x-288)-180=0
We get rid of parentheses
5x^2-24x+60x-288-180=0
We add all the numbers together, and all the variables
5x^2+36x-468=0
a = 5; b = 36; c = -468;
Δ = b2-4ac
Δ = 362-4·5·(-468)
Δ = 10656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10656}=\sqrt{144*74}=\sqrt{144}*\sqrt{74}=12\sqrt{74}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{74}}{2*5}=\frac{-36-12\sqrt{74}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{74}}{2*5}=\frac{-36+12\sqrt{74}}{10} $
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