5x2+22x=-6

Solution for 5x2+22x=-6 equation:

5x^2+22x=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x^2+22x+6=0

a = 5; b = 22; c = +6;
Δ = b2-4ac
Δ = 222-4·5·6
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{91}}{2*5}=\frac{-22-2\sqrt{91}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{91}}{2*5}=\frac{-22+2\sqrt{91}}{10}
$