(9x-10)(8x-14)=180

Solution for (9x-10)(8x-14)=180 equation:

(9x-10)(8x-14)=180

We move all terms to the left:

(9x-10)(8x-14)-(180)=0

We multiply parentheses ..

(+72x^2-126x-80x+140)-180=0

We get rid of parentheses

72x^2-126x-80x+140-180=0

We add all the numbers together, and all the variables

72x^2-206x-40=0

a = 72; b = -206; c = -40;
Δ = b2-4ac
Δ = -2062-4·72·(-40)
Δ = 53956
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:

$\sqrt{\Delta}=\sqrt{53956}=\sqrt{4*13489}=\sqrt{4}*\sqrt{13489}=2\sqrt{13489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-206)-2\sqrt{13489}}{2*72}=\frac{206-2\sqrt{13489}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-206)+2\sqrt{13489}}{2*72}=\frac{206+2\sqrt{13489}}{144}
$