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(5x-6)(7x+12)=180
We move all terms to the left:
(5x-6)(7x+12)-(180)=0
We multiply parentheses ..
(+35x^2+60x-42x-72)-180=0
We get rid of parentheses
35x^2+60x-42x-72-180=0
We add all the numbers together, and all the variables
35x^2+18x-252=0
a = 35; b = 18; c = -252;
Δ = b2-4ac
Δ = 182-4·35·(-252)
Δ = 35604
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{35604}=\sqrt{36*989}=\sqrt{36}*\sqrt{989}=6\sqrt{989}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{989}}{2*35}=\frac{-18-6\sqrt{989}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{989}}{2*35}=\frac{-18+6\sqrt{989}}{70} $
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