(6x+17)(8x+9)=180

Solution for (6x+17)(8x+9)=180 equation:

(6x+17)(8x+9)=180

We move all terms to the left:

(6x+17)(8x+9)-(180)=0

We multiply parentheses ..

(+48x^2+54x+136x+153)-180=0

We get rid of parentheses

48x^2+54x+136x+153-180=0

We add all the numbers together, and all the variables

48x^2+190x-27=0

a = 48; b = 190; c = -27;
Δ = b2-4ac
Δ = 1902-4·48·(-27)
Δ = 41284
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:

$\sqrt{\Delta}=\sqrt{41284}=\sqrt{4*10321}=\sqrt{4}*\sqrt{10321}=2\sqrt{10321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-2\sqrt{10321}}{2*48}=\frac{-190-2\sqrt{10321}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+2\sqrt{10321}}{2*48}=\frac{-190+2\sqrt{10321}}{96}
$