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(5x+8)(3x-24)=180
We move all terms to the left:
(5x+8)(3x-24)-(180)=0
We multiply parentheses ..
(+15x^2-120x+24x-192)-180=0
We get rid of parentheses
15x^2-120x+24x-192-180=0
We add all the numbers together, and all the variables
15x^2-96x-372=0
a = 15; b = -96; c = -372;
Δ = b2-4ac
Δ = -962-4·15·(-372)
Δ = 31536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31536}=\sqrt{144*219}=\sqrt{144}*\sqrt{219}=12\sqrt{219}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{219}}{2*15}=\frac{96-12\sqrt{219}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{219}}{2*15}=\frac{96+12\sqrt{219}}{30} $
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