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(19x-28)(9x+52)=180
We move all terms to the left:
(19x-28)(9x+52)-(180)=0
We multiply parentheses ..
(+171x^2+988x-252x-1456)-180=0
We get rid of parentheses
171x^2+988x-252x-1456-180=0
We add all the numbers together, and all the variables
171x^2+736x-1636=0
a = 171; b = 736; c = -1636;
Δ = b2-4ac
Δ = 7362-4·171·(-1636)
Δ = 1660720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1660720}=\sqrt{16*103795}=\sqrt{16}*\sqrt{103795}=4\sqrt{103795}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(736)-4\sqrt{103795}}{2*171}=\frac{-736-4\sqrt{103795}}{342} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(736)+4\sqrt{103795}}{2*171}=\frac{-736+4\sqrt{103795}}{342} $
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