6x2+4x=5x-3x2

Solution for 6x2+4x=5x-3x2 equation:

6x^2+4x=5x-3x^2

We move all terms to the left:

6x^2+4x-(5x-3x^2)=0

We get rid of parentheses

6x^2+3x^2-5x+4x=0

We add all the numbers together, and all the variables

9x^2-1x=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*9}=\frac{2}{18}
=1/9
$