0=x^2+6x-75

Solution for 0=x^2+6x-75 equation:

0=x^2+6x-75

We move all terms to the left:

0-(x^2+6x-75)=0

We add all the numbers together, and all the variables

-(x^2+6x-75)=0

We get rid of parentheses

-x^2-6x+75=0

We add all the numbers together, and all the variables

-1x^2-6x+75=0

a = -1; b = -6; c = +75;
Δ = b2-4ac
Δ = -62-4·(-1)·75
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{21}}{2*-1}=\frac{6-4\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{21}}{2*-1}=\frac{6+4\sqrt{21}}{-2}
$