0=8x^2-21x+12

Solution for 0=8x^2-21x+12 equation:

0=8x^2-21x+12

We move all terms to the left:

0-(8x^2-21x+12)=0

We add all the numbers together, and all the variables

-(8x^2-21x+12)=0

We get rid of parentheses

-8x^2+21x-12=0

a = -8; b = 21; c = -12;
Δ = b2-4ac
Δ = 212-4·(-8)·(-12)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{57}}{2*-8}=\frac{-21-\sqrt{57}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{57}}{2*-8}=\frac{-21+\sqrt{57}}{-16}
$