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(6x+15)(8x+7)=180
We move all terms to the left:
(6x+15)(8x+7)-(180)=0
We multiply parentheses ..
(+48x^2+42x+120x+105)-180=0
We get rid of parentheses
48x^2+42x+120x+105-180=0
We add all the numbers together, and all the variables
48x^2+162x-75=0
a = 48; b = 162; c = -75;
Δ = b2-4ac
Δ = 1622-4·48·(-75)
Δ = 40644
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40644}=\sqrt{36*1129}=\sqrt{36}*\sqrt{1129}=6\sqrt{1129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-6\sqrt{1129}}{2*48}=\frac{-162-6\sqrt{1129}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+6\sqrt{1129}}{2*48}=\frac{-162+6\sqrt{1129}}{96} $
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