(10x-4)(x-14)=180

Solution for (10x-4)(x-14)=180 equation:

(10x-4)(x-14)=180

We move all terms to the left:

(10x-4)(x-14)-(180)=0

We multiply parentheses ..

(+10x^2-140x-4x+56)-180=0

We get rid of parentheses

10x^2-140x-4x+56-180=0

We add all the numbers together, and all the variables

10x^2-144x-124=0

a = 10; b = -144; c = -124;
Δ = b2-4ac
Δ = -1442-4·10·(-124)
Δ = 25696
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:

$\sqrt{\Delta}=\sqrt{25696}=\sqrt{16*1606}=\sqrt{16}*\sqrt{1606}=4\sqrt{1606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1606}}{2*10}=\frac{144-4\sqrt{1606}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1606}}{2*10}=\frac{144+4\sqrt{1606}}{20}
$