(10x+3)(16x-18)=180

Solution for (10x+3)(16x-18)=180 equation:

(10x+3)(16x-18)=180

We move all terms to the left:

(10x+3)(16x-18)-(180)=0

We multiply parentheses ..

(+160x^2-180x+48x-54)-180=0

We get rid of parentheses

160x^2-180x+48x-54-180=0

We add all the numbers together, and all the variables

160x^2-132x-234=0

a = 160; b = -132; c = -234;
Δ = b2-4ac
Δ = -1322-4·160·(-234)
Δ = 167184
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:

$\sqrt{\Delta}=\sqrt{167184}=\sqrt{1296*129}=\sqrt{1296}*\sqrt{129}=36\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-36\sqrt{129}}{2*160}=\frac{132-36\sqrt{129}}{320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+36\sqrt{129}}{2*160}=\frac{132+36\sqrt{129}}{320}
$