0=x^2-3x-45

Solution for 0=x^2-3x-45 equation:

0=x^2-3x-45

We move all terms to the left:

0-(x^2-3x-45)=0

We add all the numbers together, and all the variables

-(x^2-3x-45)=0

We get rid of parentheses

-x^2+3x+45=0

We add all the numbers together, and all the variables

-1x^2+3x+45=0

a = -1; b = 3; c = +45;
Δ = b2-4ac
Δ = 32-4·(-1)·45
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*-1}=\frac{-3-3\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*-1}=\frac{-3+3\sqrt{21}}{-2}
$