5x^2+22x+2=-6

Solution for 5x^2+22x+2=-6 equation:

5x^2+22x+2=-6

We move all terms to the left:

5x^2+22x+2-(-6)=0

We add all the numbers together, and all the variables

5x^2+22x+8=0

a = 5; b = 22; c = +8;
Δ = b2-4ac
Δ = 222-4·5·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*5}=\frac{-4}{10}
=-2/5
$