0=2x^2+3x-189

Solution for 0=2x^2+3x-189 equation:

0=2x^2+3x-189

We move all terms to the left:

0-(2x^2+3x-189)=0

We add all the numbers together, and all the variables

-(2x^2+3x-189)=0

We get rid of parentheses

-2x^2-3x+189=0

a = -2; b = -3; c = +189;
Δ = b2-4ac
Δ = -32-4·(-2)·189
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-39}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+39}{2*-2}=\frac{42}{-4}
=-10+1/2
$