2x2+33x=54

Solution for 2x2+33x=54 equation:

2x^2+33x=54

We move all terms to the left:

2x^2+33x-(54)=0

a = 2; b = 33; c = -54;
Δ = b2-4ac
Δ = 332-4·2·(-54)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-39}{2*2}=\frac{-72}{4}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+39}{2*2}=\frac{6}{4}
=1+1/2
$