2x(x+27)=6x

Solution for 2x(x+27)=6x equation:

2x(x+27)=6x

We move all terms to the left:

2x(x+27)-(6x)=0

We add all the numbers together, and all the variables

-6x+2x(x+27)=0

We multiply parentheses

2x^2-6x+54x=0

We add all the numbers together, and all the variables

2x^2+48x=0

a = 2; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·2·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*2}=\frac{-96}{4}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*2}=\frac{0}{4}
=0
$