3x(4x-8)=5x(2x+6)

Solution for 3x(4x-8)=5x(2x+6) equation:

3x(4x-8)=5x(2x+6)

We move all terms to the left:

3x(4x-8)-(5x(2x+6))=0

We multiply parentheses

12x^2-24x-(5x(2x+6))=0


We calculate terms in parentheses: -(5x(2x+6)), so:

5x(2x+6)

We multiply parentheses

10x^2+30x

Back to the equation:

-(10x^2+30x)


We get rid of parentheses

12x^2-10x^2-24x-30x=0

We add all the numbers together, and all the variables

2x^2-54x=0

a = 2; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·2·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*2}=\frac{108}{4}
=27
$