6x^2+3x+2x^2=-5x-7x^2

Solution for 6x^2+3x+2x^2=-5x-7x^2 equation:

6x^2+3x+2x^2=-5x-7x^2

We move all terms to the left:

6x^2+3x+2x^2-(-5x-7x^2)=0

We add all the numbers together, and all the variables

8x^2-(-5x-7x^2)+3x=0

We get rid of parentheses

8x^2+7x^2+5x+3x=0

We add all the numbers together, and all the variables

15x^2+8x=0

a = 15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·15·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*15}=\frac{-16}{30}
=-8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*15}=\frac{0}{30}
=0
$