(6x-1)(4x-7)=180

Solution for (6x-1)(4x-7)=180 equation:

(6x-1)(4x-7)=180

We move all terms to the left:

(6x-1)(4x-7)-(180)=0

We multiply parentheses ..

(+24x^2-42x-4x+7)-180=0

We get rid of parentheses

24x^2-42x-4x+7-180=0

We add all the numbers together, and all the variables

24x^2-46x-173=0

a = 24; b = -46; c = -173;
Δ = b2-4ac
Δ = -462-4·24·(-173)
Δ = 18724
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:

$\sqrt{\Delta}=\sqrt{18724}=\sqrt{4*4681}=\sqrt{4}*\sqrt{4681}=2\sqrt{4681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{4681}}{2*24}=\frac{46-2\sqrt{4681}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{4681}}{2*24}=\frac{46+2\sqrt{4681}}{48}
$