54=x(2x+3)

Solution for 54=x(2x+3) equation:

54=x(2x+3)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(2x+3)), so:

x(2x+3)

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


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