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(9x-77)(3x+7)=180
We move all terms to the left:
(9x-77)(3x+7)-(180)=0
We multiply parentheses ..
(+27x^2+63x-231x-539)-180=0
We get rid of parentheses
27x^2+63x-231x-539-180=0
We add all the numbers together, and all the variables
27x^2-168x-719=0
a = 27; b = -168; c = -719;
Δ = b2-4ac
Δ = -1682-4·27·(-719)
Δ = 105876
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{105876}=\sqrt{36*2941}=\sqrt{36}*\sqrt{2941}=6\sqrt{2941}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-6\sqrt{2941}}{2*27}=\frac{168-6\sqrt{2941}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+6\sqrt{2941}}{2*27}=\frac{168+6\sqrt{2941}}{54} $
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