5x(x+12)=4x(x+3)

Solution for 5x(x+12)=4x(x+3) equation:

5x(x+12)=4x(x+3)

We move all terms to the left:

5x(x+12)-(4x(x+3))=0

We multiply parentheses

5x^2+60x-(4x(x+3))=0


We calculate terms in parentheses: -(4x(x+3)), so:

4x(x+3)

We multiply parentheses

4x^2+12x

Back to the equation:

-(4x^2+12x)


We get rid of parentheses

5x^2-4x^2+60x-12x=0

We add all the numbers together, and all the variables

x^2+48x=0

a = 1; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·1·0
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*1}=\frac{-96}{2}
=-48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*1}=\frac{0}{2}
=0
$