X^2+3x=-5x^2-4x

Solution for X^2+3x=-5x^2-4x equation:

X^2+3X=-5X^2-4X

We move all terms to the left:

X^2+3X-(-5X^2-4X)=0

We get rid of parentheses

X^2+5X^2+4X+3X=0

We add all the numbers together, and all the variables

6X^2+7X=0

a = 6; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*6}=\frac{-14}{12}
=-1+1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*6}=\frac{0}{12}
=0
$