0=x^2-10x-12

Solution for 0=x^2-10x-12 equation:

0=x^2-10x-12

We move all terms to the left:

0-(x^2-10x-12)=0

We add all the numbers together, and all the variables

-(x^2-10x-12)=0

We get rid of parentheses

-x^2+10x+12=0

We add all the numbers together, and all the variables

-1x^2+10x+12=0

a = -1; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·(-1)·12
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{37}}{2*-1}=\frac{-10-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{37}}{2*-1}=\frac{-10+2\sqrt{37}}{-2}
$