3x^2-21x=8

Solution for 3x^2-21x=8 equation:

3x^2-21x=8

We move all terms to the left:

3x^2-21x-(8)=0

a = 3; b = -21; c = -8;
Δ = b2-4ac
Δ = -212-4·3·(-8)
Δ = 537
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{537}}{2*3}=\frac{21-\sqrt{537}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{537}}{2*3}=\frac{21+\sqrt{537}}{6}
$