2(x^2)=(54-3x)

Solution for 2(x^2)=(54-3x) equation:

2(x^2)=(54-3x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -((-3x+54)), so:

(-3x+54)

We get rid of parentheses

-3x+54

Back to the equation:

-(-3x+54)


We get rid of parentheses

2x^2+3x-54=0

a = 2; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*2}=\frac{18}{4}
=4+1/2
$