4x(12x+7)=5x(12x-4)

Solution for 4x(12x+7)=5x(12x-4) equation:

4x(12x+7)=5x(12x-4)

We move all terms to the left:

4x(12x+7)-(5x(12x-4))=0

We multiply parentheses

48x^2+28x-(5x(12x-4))=0


We calculate terms in parentheses: -(5x(12x-4)), so:

5x(12x-4)

We multiply parentheses

60x^2-20x

Back to the equation:

-(60x^2-20x)


We get rid of parentheses

48x^2-60x^2+28x+20x=0

We add all the numbers together, and all the variables

-12x^2+48x=0

a = -12; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-12)·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*-12}=\frac{-96}{-24}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-12}=\frac{0}{-24}
=0
$