(1+6x)(2x-13)=180

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Solution for (1+6x)(2x-13)=180 equation:



(1+6x)(2x-13)=180
We move all terms to the left:
(1+6x)(2x-13)-(180)=0
We add all the numbers together, and all the variables
(6x+1)(2x-13)-180=0
We multiply parentheses ..
(+12x^2-78x+2x-13)-180=0
We get rid of parentheses
12x^2-78x+2x-13-180=0
We add all the numbers together, and all the variables
12x^2-76x-193=0
a = 12; b = -76; c = -193;
Δ = b2-4ac
Δ = -762-4·12·(-193)
Δ = 15040
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:
$\sqrt{\Delta}=\sqrt{15040}=\sqrt{64*235}=\sqrt{64}*\sqrt{235}=8\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-8\sqrt{235}}{2*12}=\frac{76-8\sqrt{235}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+8\sqrt{235}}{2*12}=\frac{76+8\sqrt{235}}{24} $

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