x^2-10x+12=2x+5

Solution for x^2-10x+12=2x+5 equation:

x^2-10x+12=2x+5

We move all terms to the left:

x^2-10x+12-(2x+5)=0

We get rid of parentheses

x^2-10x-2x-5+12=0

We add all the numbers together, and all the variables

x^2-12x+7=0

a = 1; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·1·7
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{29}}{2*1}=\frac{12-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{29}}{2*1}=\frac{12+2\sqrt{29}}{2}
$