5x^2+16x=-6

Solution for 5x^2+16x=-6 equation:

5x^2+16x=-6

We move all terms to the left:

5x^2+16x-(-6)=0

We add all the numbers together, and all the variables

5x^2+16x+6=0

a = 5; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·5·6
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{34}}{2*5}=\frac{-16-2\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{34}}{2*5}=\frac{-16+2\sqrt{34}}{10}
$