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(4x-4)(5x+1)41=180
We move all terms to the left:
(4x-4)(5x+1)41-(180)=0
We multiply parentheses ..
(+20x^2+4x-20x-4)41-180=0
We multiply parentheses
820x^2+164x-820x-164-180=0
We add all the numbers together, and all the variables
820x^2-656x-344=0
a = 820; b = -656; c = -344;
Δ = b2-4ac
Δ = -6562-4·820·(-344)
Δ = 1558656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1558656}=\sqrt{576*2706}=\sqrt{576}*\sqrt{2706}=24\sqrt{2706}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-656)-24\sqrt{2706}}{2*820}=\frac{656-24\sqrt{2706}}{1640} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-656)+24\sqrt{2706}}{2*820}=\frac{656+24\sqrt{2706}}{1640} $
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