3x^2=21x+54

Solution for 3x^2=21x+54 equation:

3x^2=21x+54

We move all terms to the left:

3x^2-(21x+54)=0

We get rid of parentheses

3x^2-21x-54=0

a = 3; b = -21; c = -54;
Δ = b2-4ac
Δ = -212-4·3·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-33}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+33}{2*3}=\frac{54}{6}
=9
$