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(9x+17)(3x+7)=180
We move all terms to the left:
(9x+17)(3x+7)-(180)=0
We multiply parentheses ..
(+27x^2+63x+51x+119)-180=0
We get rid of parentheses
27x^2+63x+51x+119-180=0
We add all the numbers together, and all the variables
27x^2+114x-61=0
a = 27; b = 114; c = -61;
Δ = b2-4ac
Δ = 1142-4·27·(-61)
Δ = 19584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-24\sqrt{34}}{2*27}=\frac{-114-24\sqrt{34}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+24\sqrt{34}}{2*27}=\frac{-114+24\sqrt{34}}{54} $
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