0=4x^2-6x-8

Solution for 0=4x^2-6x-8 equation:

0=4x^2-6x-8

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -4; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-4)·8
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{41}}{2*-4}=\frac{-6-2\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{41}}{2*-4}=\frac{-6+2\sqrt{41}}{-8}
$