(6x-17)(4x+9)+x+x=360

Solution for (6x-17)(4x+9)+x+x=360 equation:

(6x-17)(4x+9)+x+x=360

We move all terms to the left:

(6x-17)(4x+9)+x+x-(360)=0

We add all the numbers together, and all the variables

2x+(6x-17)(4x+9)-360=0

We multiply parentheses ..

(+24x^2+54x-68x-153)+2x-360=0

We get rid of parentheses

24x^2+54x-68x+2x-153-360=0

We add all the numbers together, and all the variables

24x^2-12x-513=0

a = 24; b = -12; c = -513;
Δ = b2-4ac
Δ = -122-4·24·(-513)
Δ = 49392
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:

$\sqrt{\Delta}=\sqrt{49392}=\sqrt{7056*7}=\sqrt{7056}*\sqrt{7}=84\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-84\sqrt{7}}{2*24}=\frac{12-84\sqrt{7}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+84\sqrt{7}}{2*24}=\frac{12+84\sqrt{7}}{48}
$