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(13x-46)(7x-14)=180
We move all terms to the left:
(13x-46)(7x-14)-(180)=0
We multiply parentheses ..
(+91x^2-182x-322x+644)-180=0
We get rid of parentheses
91x^2-182x-322x+644-180=0
We add all the numbers together, and all the variables
91x^2-504x+464=0
a = 91; b = -504; c = +464;
Δ = b2-4ac
Δ = -5042-4·91·464
Δ = 85120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{85120}=\sqrt{64*1330}=\sqrt{64}*\sqrt{1330}=8\sqrt{1330}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-8\sqrt{1330}}{2*91}=\frac{504-8\sqrt{1330}}{182} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+8\sqrt{1330}}{2*91}=\frac{504+8\sqrt{1330}}{182} $
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