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(3x-19)(3x-19)+75=180
We move all terms to the left:
(3x-19)(3x-19)+75-(180)=0
We add all the numbers together, and all the variables
(3x-19)(3x-19)-105=0
We multiply parentheses ..
(+9x^2-57x-57x+361)-105=0
We get rid of parentheses
9x^2-57x-57x+361-105=0
We add all the numbers together, and all the variables
9x^2-114x+256=0
a = 9; b = -114; c = +256;
Δ = b2-4ac
Δ = -1142-4·9·256
Δ = 3780
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{105}}{2*9}=\frac{114-6\sqrt{105}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{105}}{2*9}=\frac{114+6\sqrt{105}}{18} $
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