6a^2+10a+12=10

Solution for 6a^2+10a+12=10 equation:

6a^2+10a+12=10

We move all terms to the left:

6a^2+10a+12-(10)=0

We add all the numbers together, and all the variables

6a^2+10a+2=0

a = 6; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·6·2
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*6}=\frac{-10-2\sqrt{13}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*6}=\frac{-10+2\sqrt{13}}{12}
$