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(5x-18)(3x+42)=180
We move all terms to the left:
(5x-18)(3x+42)-(180)=0
We multiply parentheses ..
(+15x^2+210x-54x-756)-180=0
We get rid of parentheses
15x^2+210x-54x-756-180=0
We add all the numbers together, and all the variables
15x^2+156x-936=0
a = 15; b = 156; c = -936;
Δ = b2-4ac
Δ = 1562-4·15·(-936)
Δ = 80496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80496}=\sqrt{144*559}=\sqrt{144}*\sqrt{559}=12\sqrt{559}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-12\sqrt{559}}{2*15}=\frac{-156-12\sqrt{559}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+12\sqrt{559}}{2*15}=\frac{-156+12\sqrt{559}}{30} $
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