0=6x^2+8x

Solution for 0=6x^2+8x equation:

0=6x^2+8x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-6x^2-8x=0

a = -6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-6)·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*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-6}=\frac{16}{-12}
=-1+1/3
$