6x^2+12x=5+3

Solution for 6x^2+12x=5+3 equation:

6x^2+12x=5+3

We move all terms to the left:

6x^2+12x-(5+3)=0

We add all the numbers together, and all the variables

6x^2+12x-8=0

a = 6; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*6}=\frac{-12-4\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*6}=\frac{-12+4\sqrt{21}}{12}
$