(7x-18)(5x+11)=0

Solution for (7x-18)(5x+11)=0 equation:

(7x-18)(5x+11)=0

We multiply parentheses ..

(+35x^2+77x-90x-198)=0

We get rid of parentheses

35x^2+77x-90x-198=0

We add all the numbers together, and all the variables

35x^2-13x-198=0

a = 35; b = -13; c = -198;
Δ = b2-4ac
Δ = -132-4·35·(-198)
Δ = 27889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27889}=167$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-167}{2*35}=\frac{-154}{70}
=-2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+167}{2*35}=\frac{180}{70}
=2+4/7
$