(6x-7)(4x-23)=180

Solution for (6x-7)(4x-23)=180 equation:

(6x-7)(4x-23)=180

We move all terms to the left:

(6x-7)(4x-23)-(180)=0

We multiply parentheses ..

(+24x^2-138x-28x+161)-180=0

We get rid of parentheses

24x^2-138x-28x+161-180=0

We add all the numbers together, and all the variables

24x^2-166x-19=0

a = 24; b = -166; c = -19;
Δ = b2-4ac
Δ = -1662-4·24·(-19)
Δ = 29380
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:

$\sqrt{\Delta}=\sqrt{29380}=\sqrt{4*7345}=\sqrt{4}*\sqrt{7345}=2\sqrt{7345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-2\sqrt{7345}}{2*24}=\frac{166-2\sqrt{7345}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+2\sqrt{7345}}{2*24}=\frac{166+2\sqrt{7345}}{48}
$