3x^2+22x+13=0

Solution for 3x^2+22x+13=0 equation:

3x^2+22x+13=0

a = 3; b = 22; c = +13;
Δ = b2-4ac
Δ = 222-4·3·13
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{82}}{2*3}=\frac{-22-2\sqrt{82}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{82}}{2*3}=\frac{-22+2\sqrt{82}}{6}
$