3a^2+12a-22=0

Solution for 3a^2+12a-22=0 equation:

3a^2+12a-22=0

a = 3; b = 12; c = -22;
Δ = b2-4ac
Δ = 122-4·3·(-22)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{102}}{2*3}=\frac{-12-2\sqrt{102}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{102}}{2*3}=\frac{-12+2\sqrt{102}}{6}
$