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(8x-7)(x+16)=180
We move all terms to the left:
(8x-7)(x+16)-(180)=0
We multiply parentheses ..
(+8x^2+128x-7x-112)-180=0
We get rid of parentheses
8x^2+128x-7x-112-180=0
We add all the numbers together, and all the variables
8x^2+121x-292=0
a = 8; b = 121; c = -292;
Δ = b2-4ac
Δ = 1212-4·8·(-292)
Δ = 23985
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23985}=\sqrt{9*2665}=\sqrt{9}*\sqrt{2665}=3\sqrt{2665}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-3\sqrt{2665}}{2*8}=\frac{-121-3\sqrt{2665}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+3\sqrt{2665}}{2*8}=\frac{-121+3\sqrt{2665}}{16} $
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