-4x^2+6x=-8x-3x^2

Solution for -4x^2+6x=-8x-3x^2 equation:

-4x^2+6x=-8x-3x^2

We move all terms to the left:

-4x^2+6x-(-8x-3x^2)=0

We get rid of parentheses

-4x^2+3x^2+8x+6x=0

We add all the numbers together, and all the variables

-1x^2+14x=0

a = -1; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-1)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-1}=\frac{0}{-2}
=0
$