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(5x+7)(8x-71)=90
We move all terms to the left:
(5x+7)(8x-71)-(90)=0
We multiply parentheses ..
(+40x^2-355x+56x-497)-90=0
We get rid of parentheses
40x^2-355x+56x-497-90=0
We add all the numbers together, and all the variables
40x^2-299x-587=0
a = 40; b = -299; c = -587;
Δ = b2-4ac
Δ = -2992-4·40·(-587)
Δ = 183321
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{183321}=\sqrt{9*20369}=\sqrt{9}*\sqrt{20369}=3\sqrt{20369}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-3\sqrt{20369}}{2*40}=\frac{299-3\sqrt{20369}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+3\sqrt{20369}}{2*40}=\frac{299+3\sqrt{20369}}{80} $
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