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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-20x-(2x(x+3))=0


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

2x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

4x^2-2x^2-20x-6x=0

We add all the numbers together, and all the variables

2x^2-26x=0

a = 2; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·2·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*2}=\frac{52}{4}
=13
$