3x+5x^2=-7x^2

Solution for 3x+5x^2=-7x^2 equation:

3x+5x^2=-7x^2

We move all terms to the left:

3x+5x^2-(-7x^2)=0

We get rid of parentheses

5x^2+7x^2+3x=0

We add all the numbers together, and all the variables

12x^2+3x=0

a = 12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·12·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*12}=\frac{0}{24}
=0
$