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(9x+12)3x-11=2x-2
We move all terms to the left:
(9x+12)3x-11-(2x-2)=0
We multiply parentheses
27x^2+36x-(2x-2)-11=0
We get rid of parentheses
27x^2+36x-2x+2-11=0
We add all the numbers together, and all the variables
27x^2+34x-9=0
a = 27; b = 34; c = -9;
Δ = b2-4ac
Δ = 342-4·27·(-9)
Δ = 2128
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-4\sqrt{133}}{2*27}=\frac{-34-4\sqrt{133}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+4\sqrt{133}}{2*27}=\frac{-34+4\sqrt{133}}{54} $
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