0=18x^2+5x-7

Solution for 0=18x^2+5x-7 equation:

0=18x^2+5x-7

We move all terms to the left:

0-(18x^2+5x-7)=0

We add all the numbers together, and all the variables

-(18x^2+5x-7)=0

We get rid of parentheses

-18x^2-5x+7=0

a = -18; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-18)·7
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*-18}=\frac{-18}{-36}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*-18}=\frac{28}{-36}
=-7/9
$