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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+10x+5=0

a = 1; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·1·5
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*1}=\frac{-10-4\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*1}=\frac{-10+4\sqrt{5}}{2}
$