x2+8x+12x=10

Solution for x2+8x+12x=10 equation:

x2+8x+12x=10

We move all terms to the left:

x2+8x+12x-(10)=0

We add all the numbers together, and all the variables

x^2+20x-10=0

a = 1; b = 20; c = -10;
Δ = b2-4ac
Δ = 202-4·1·(-10)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{110}}{2*1}=\frac{-20-2\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{110}}{2*1}=\frac{-20+2\sqrt{110}}{2}
$