(8x-2)(9x-14)=180

Solution for (8x-2)(9x-14)=180 equation:

(8x-2)(9x-14)=180

We move all terms to the left:

(8x-2)(9x-14)-(180)=0

We multiply parentheses ..

(+72x^2-112x-18x+28)-180=0

We get rid of parentheses

72x^2-112x-18x+28-180=0

We add all the numbers together, and all the variables

72x^2-130x-152=0

a = 72; b = -130; c = -152;
Δ = b2-4ac
Δ = -1302-4·72·(-152)
Δ = 60676
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:

$\sqrt{\Delta}=\sqrt{60676}=\sqrt{4*15169}=\sqrt{4}*\sqrt{15169}=2\sqrt{15169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{15169}}{2*72}=\frac{130-2\sqrt{15169}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{15169}}{2*72}=\frac{130+2\sqrt{15169}}{144}
$