(2x-3)(2x-3)=135

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Solution for (2x-3)(2x-3)=135 equation:



(2x-3)(2x-3)=135
We move all terms to the left:
(2x-3)(2x-3)-(135)=0
We multiply parentheses ..
(+4x^2-6x-6x+9)-135=0
We get rid of parentheses
4x^2-6x-6x+9-135=0
We add all the numbers together, and all the variables
4x^2-12x-126=0
a = 4; b = -12; c = -126;
Δ = b2-4ac
Δ = -122-4·4·(-126)
Δ = 2160
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:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{15}}{2*4}=\frac{12-12\sqrt{15}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{15}}{2*4}=\frac{12+12\sqrt{15}}{8} $

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