0=2x^2-6x-45

Solution for 0=2x^2-6x-45 equation:

0=2x^2-6x-45

We move all terms to the left:

0-(2x^2-6x-45)=0

We add all the numbers together, and all the variables

-(2x^2-6x-45)=0

We get rid of parentheses

-2x^2+6x+45=0

a = -2; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-2)·45
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*-2}=\frac{-6-6\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*-2}=\frac{-6+6\sqrt{11}}{-4}
$