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(12x+1)(4x-13)=180x
We move all terms to the left:
(12x+1)(4x-13)-(180x)=0
We add all the numbers together, and all the variables
-180x+(12x+1)(4x-13)=0
We multiply parentheses ..
(+48x^2-156x+4x-13)-180x=0
We get rid of parentheses
48x^2-156x+4x-180x-13=0
We add all the numbers together, and all the variables
48x^2-332x-13=0
a = 48; b = -332; c = -13;
Δ = b2-4ac
Δ = -3322-4·48·(-13)
Δ = 112720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112720}=\sqrt{16*7045}=\sqrt{16}*\sqrt{7045}=4\sqrt{7045}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-332)-4\sqrt{7045}}{2*48}=\frac{332-4\sqrt{7045}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-332)+4\sqrt{7045}}{2*48}=\frac{332+4\sqrt{7045}}{96} $
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