6x^2+22x+18=0

Solution for 6x^2+22x+18=0 equation:

6x^2+22x+18=0

a = 6; b = 22; c = +18;
Δ = b2-4ac
Δ = 222-4·6·18
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{13}}{2*6}=\frac{-22-2\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{13}}{2*6}=\frac{-22+2\sqrt{13}}{12}
$