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(12x+1)(4x-13)=180
We move all terms to the left:
(12x+1)(4x-13)-(180)=0
We multiply parentheses ..
(+48x^2-156x+4x-13)-180=0
We get rid of parentheses
48x^2-156x+4x-13-180=0
We add all the numbers together, and all the variables
48x^2-152x-193=0
a = 48; b = -152; c = -193;
Δ = b2-4ac
Δ = -1522-4·48·(-193)
Δ = 60160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60160}=\sqrt{256*235}=\sqrt{256}*\sqrt{235}=16\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-16\sqrt{235}}{2*48}=\frac{152-16\sqrt{235}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+16\sqrt{235}}{2*48}=\frac{152+16\sqrt{235}}{96} $
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