(6x+7)(8x-17)=180

Solution for (6x+7)(8x-17)=180 equation:

(6x+7)(8x-17)=180

We move all terms to the left:

(6x+7)(8x-17)-(180)=0

We multiply parentheses ..

(+48x^2-102x+56x-119)-180=0

We get rid of parentheses

48x^2-102x+56x-119-180=0

We add all the numbers together, and all the variables

48x^2-46x-299=0

a = 48; b = -46; c = -299;
Δ = b2-4ac
Δ = -462-4·48·(-299)
Δ = 59524
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:

$\sqrt{\Delta}=\sqrt{59524}=\sqrt{4*14881}=\sqrt{4}*\sqrt{14881}=2\sqrt{14881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{14881}}{2*48}=\frac{46-2\sqrt{14881}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{14881}}{2*48}=\frac{46+2\sqrt{14881}}{96}
$