0=10x^2+18x-45

Solution for 0=10x^2+18x-45 equation:

0=10x^2+18x-45

We move all terms to the left:

0-(10x^2+18x-45)=0

We add all the numbers together, and all the variables

-(10x^2+18x-45)=0

We get rid of parentheses

-10x^2-18x+45=0

a = -10; b = -18; c = +45;
Δ = b2-4ac
Δ = -182-4·(-10)·45
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{59}}{2*-10}=\frac{18-6\sqrt{59}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{59}}{2*-10}=\frac{18+6\sqrt{59}}{-20}
$