2a^2+3a=-5a^2

Solution for 2a^2+3a=-5a^2 equation:

2a^2+3a=-5a^2

We move all terms to the left:

2a^2+3a-(-5a^2)=0

We get rid of parentheses

2a^2+5a^2+3a=0

We add all the numbers together, and all the variables

7a^2+3a=0

a = 7; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·7·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*7}=\frac{-6}{14}
=-3/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*7}=\frac{0}{14}
=0
$