0x=8x^2+53x-21

Solution for 0x=8x^2+53x-21 equation:

0x=8x^2+53x-21

We move all terms to the left:

0x-(8x^2+53x-21)=0

We add all the numbers together, and all the variables

x-(8x^2+53x-21)=0

We get rid of parentheses

-8x^2+x-53x+21=0

We add all the numbers together, and all the variables

-8x^2-52x+21=0

a = -8; b = -52; c = +21;
Δ = b2-4ac
Δ = -522-4·(-8)·21
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{211}}{2*-8}=\frac{52-4\sqrt{211}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{211}}{2*-8}=\frac{52+4\sqrt{211}}{-16}
$