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(4x-18)(6x-18)=90
We move all terms to the left:
(4x-18)(6x-18)-(90)=0
We multiply parentheses ..
(+24x^2-72x-108x+324)-90=0
We get rid of parentheses
24x^2-72x-108x+324-90=0
We add all the numbers together, and all the variables
24x^2-180x+234=0
a = 24; b = -180; c = +234;
Δ = b2-4ac
Δ = -1802-4·24·234
Δ = 9936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{69}}{2*24}=\frac{180-12\sqrt{69}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{69}}{2*24}=\frac{180+12\sqrt{69}}{48} $
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