5w2=-8w-3

Solution for 5w2=-8w-3 equation:

5w^2=-8w-3

We move all terms to the left:

5w^2-(-8w-3)=0

We get rid of parentheses

5w^2+8w+3=0

a = 5; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·5·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*5}=\frac{-10}{10}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*5}=\frac{-6}{10}
=-3/5
$