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(6x-1)(3x-8)=180
We move all terms to the left:
(6x-1)(3x-8)-(180)=0
We multiply parentheses ..
(+18x^2-48x-3x+8)-180=0
We get rid of parentheses
18x^2-48x-3x+8-180=0
We add all the numbers together, and all the variables
18x^2-51x-172=0
a = 18; b = -51; c = -172;
Δ = b2-4ac
Δ = -512-4·18·(-172)
Δ = 14985
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14985}=\sqrt{81*185}=\sqrt{81}*\sqrt{185}=9\sqrt{185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-9\sqrt{185}}{2*18}=\frac{51-9\sqrt{185}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+9\sqrt{185}}{2*18}=\frac{51+9\sqrt{185}}{36} $
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