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(5x+7)(8x-71)=180
We move all terms to the left:
(5x+7)(8x-71)-(180)=0
We multiply parentheses ..
(+40x^2-355x+56x-497)-180=0
We get rid of parentheses
40x^2-355x+56x-497-180=0
We add all the numbers together, and all the variables
40x^2-299x-677=0
a = 40; b = -299; c = -677;
Δ = b2-4ac
Δ = -2992-4·40·(-677)
Δ = 197721
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{197721}=\sqrt{81*2441}=\sqrt{81}*\sqrt{2441}=9\sqrt{2441}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-9\sqrt{2441}}{2*40}=\frac{299-9\sqrt{2441}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+9\sqrt{2441}}{2*40}=\frac{299+9\sqrt{2441}}{80} $
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