5x^2=-10x-4

Solution for 5x^2=-10x-4 equation:

5x^2=-10x-4

We move all terms to the left:

5x^2-(-10x-4)=0

We get rid of parentheses

5x^2+10x+4=0

a = 5; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·5·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*5}=\frac{-10-2\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*5}=\frac{-10+2\sqrt{5}}{10}
$