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(3x-4)(3x-4)-2=11
We move all terms to the left:
(3x-4)(3x-4)-2-(11)=0
We add all the numbers together, and all the variables
(3x-4)(3x-4)-13=0
We multiply parentheses ..
(+9x^2-12x-12x+16)-13=0
We get rid of parentheses
9x^2-12x-12x+16-13=0
We add all the numbers together, and all the variables
9x^2-24x+3=0
a = 9; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·9·3
Δ = 468
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{13}}{2*9}=\frac{24-6\sqrt{13}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{13}}{2*9}=\frac{24+6\sqrt{13}}{18} $
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