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(9x+24)(6x-24)=180
We move all terms to the left:
(9x+24)(6x-24)-(180)=0
We multiply parentheses ..
(+54x^2-216x+144x-576)-180=0
We get rid of parentheses
54x^2-216x+144x-576-180=0
We add all the numbers together, and all the variables
54x^2-72x-756=0
a = 54; b = -72; c = -756;
Δ = b2-4ac
Δ = -722-4·54·(-756)
Δ = 168480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{168480}=\sqrt{1296*130}=\sqrt{1296}*\sqrt{130}=36\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-36\sqrt{130}}{2*54}=\frac{72-36\sqrt{130}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+36\sqrt{130}}{2*54}=\frac{72+36\sqrt{130}}{108} $
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