0=-8x^2-11x+54

Solution for 0=-8x^2-11x+54 equation:

0=-8x^2-11x+54

We move all terms to the left:

0-(-8x^2-11x+54)=0

We add all the numbers together, and all the variables

-(-8x^2-11x+54)=0

We get rid of parentheses

8x^2+11x-54=0

a = 8; b = 11; c = -54;
Δ = b2-4ac
Δ = 112-4·8·(-54)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-43}{2*8}=\frac{-54}{16}
=-3+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+43}{2*8}=\frac{32}{16}
=2
$