(7x-2)+18x(11x-34)=180

Solution for (7x-2)+18x(11x-34)=180 equation:

(7x-2)+18x(11x-34)=180

We move all terms to the left:

(7x-2)+18x(11x-34)-(180)=0

We multiply parentheses

198x^2+(7x-2)-612x-180=0

We get rid of parentheses

198x^2+7x-612x-2-180=0

We add all the numbers together, and all the variables

198x^2-605x-182=0

a = 198; b = -605; c = -182;
Δ = b2-4ac
Δ = -6052-4·198·(-182)
Δ = 510169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-605)-\sqrt{510169}}{2*198}=\frac{605-\sqrt{510169}}{396}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-605)+\sqrt{510169}}{2*198}=\frac{605+\sqrt{510169}}{396}
$