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(9x+6)(6x+9)=130
We move all terms to the left:
(9x+6)(6x+9)-(130)=0
We multiply parentheses ..
(+54x^2+81x+36x+54)-130=0
We get rid of parentheses
54x^2+81x+36x+54-130=0
We add all the numbers together, and all the variables
54x^2+117x-76=0
a = 54; b = 117; c = -76;
Δ = b2-4ac
Δ = 1172-4·54·(-76)
Δ = 30105
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30105}=\sqrt{9*3345}=\sqrt{9}*\sqrt{3345}=3\sqrt{3345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-3\sqrt{3345}}{2*54}=\frac{-117-3\sqrt{3345}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+3\sqrt{3345}}{2*54}=\frac{-117+3\sqrt{3345}}{108} $
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