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(3x-4)(3x-17)+69=180
We move all terms to the left:
(3x-4)(3x-17)+69-(180)=0
We add all the numbers together, and all the variables
(3x-4)(3x-17)-111=0
We multiply parentheses ..
(+9x^2-51x-12x+68)-111=0
We get rid of parentheses
9x^2-51x-12x+68-111=0
We add all the numbers together, and all the variables
9x^2-63x-43=0
a = 9; b = -63; c = -43;
Δ = b2-4ac
Δ = -632-4·9·(-43)
Δ = 5517
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5517}=\sqrt{9*613}=\sqrt{9}*\sqrt{613}=3\sqrt{613}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{613}}{2*9}=\frac{63-3\sqrt{613}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{613}}{2*9}=\frac{63+3\sqrt{613}}{18} $
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