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 = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*-1}=\frac{-10-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*-1}=\frac{-10+2\sqrt{13}}{-2}
$