5x(3x+2)=7x(5x-2)

Solution for 5x(3x+2)=7x(5x-2) equation:

5x(3x+2)=7x(5x-2)

We move all terms to the left:

5x(3x+2)-(7x(5x-2))=0

We multiply parentheses

15x^2+10x-(7x(5x-2))=0


We calculate terms in parentheses: -(7x(5x-2)), so:

7x(5x-2)

We multiply parentheses

35x^2-14x

Back to the equation:

-(35x^2-14x)


We get rid of parentheses

15x^2-35x^2+10x+14x=0

We add all the numbers together, and all the variables

-20x^2+24x=0

a = -20; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-20)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-20}=\frac{-48}{-40}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-20}=\frac{0}{-40}
=0
$