(12x-9)(17x+3)=260

Solution for (12x-9)(17x+3)=260 equation:

(12x-9)(17x+3)=260

We move all terms to the left:

(12x-9)(17x+3)-(260)=0

We multiply parentheses ..

(+204x^2+36x-153x-27)-260=0

We get rid of parentheses

204x^2+36x-153x-27-260=0

We add all the numbers together, and all the variables

204x^2-117x-287=0

a = 204; b = -117; c = -287;
Δ = b2-4ac
Δ = -1172-4·204·(-287)
Δ = 247881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-\sqrt{247881}}{2*204}=\frac{117-\sqrt{247881}}{408}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+\sqrt{247881}}{2*204}=\frac{117+\sqrt{247881}}{408}
$