(12x-9)(17x+3)=360

Solution for (12x-9)(17x+3)=360 equation:

(12x-9)(17x+3)=360

We move all terms to the left:

(12x-9)(17x+3)-(360)=0

We multiply parentheses ..

(+204x^2+36x-153x-27)-360=0

We get rid of parentheses

204x^2+36x-153x-27-360=0

We add all the numbers together, and all the variables

204x^2-117x-387=0

a = 204; b = -117; c = -387;
Δ = b2-4ac
Δ = -1172-4·204·(-387)
Δ = 329481
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:

$\sqrt{\Delta}=\sqrt{329481}=\sqrt{9*36609}=\sqrt{9}*\sqrt{36609}=3\sqrt{36609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-3\sqrt{36609}}{2*204}=\frac{117-3\sqrt{36609}}{408}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+3\sqrt{36609}}{2*204}=\frac{117+3\sqrt{36609}}{408}
$