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(9x+4)(3x-2)=180
We move all terms to the left:
(9x+4)(3x-2)-(180)=0
We multiply parentheses ..
(+27x^2-18x+12x-8)-180=0
We get rid of parentheses
27x^2-18x+12x-8-180=0
We add all the numbers together, and all the variables
27x^2-6x-188=0
a = 27; b = -6; c = -188;
Δ = b2-4ac
Δ = -62-4·27·(-188)
Δ = 20340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20340}=\sqrt{36*565}=\sqrt{36}*\sqrt{565}=6\sqrt{565}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{565}}{2*27}=\frac{6-6\sqrt{565}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{565}}{2*27}=\frac{6+6\sqrt{565}}{54} $
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