(8x-61)(7x+1)=180

Solution for (8x-61)(7x+1)=180 equation:

(8x-61)(7x+1)=180

We move all terms to the left:

(8x-61)(7x+1)-(180)=0

We multiply parentheses ..

(+56x^2+8x-427x-61)-180=0

We get rid of parentheses

56x^2+8x-427x-61-180=0

We add all the numbers together, and all the variables

56x^2-419x-241=0

a = 56; b = -419; c = -241;
Δ = b2-4ac
Δ = -4192-4·56·(-241)
Δ = 229545
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:

$\sqrt{\Delta}=\sqrt{229545}=\sqrt{9*25505}=\sqrt{9}*\sqrt{25505}=3\sqrt{25505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-419)-3\sqrt{25505}}{2*56}=\frac{419-3\sqrt{25505}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-419)+3\sqrt{25505}}{2*56}=\frac{419+3\sqrt{25505}}{112}
$