5x(3x-4)-3x(4x-2)=2x(5x+7)

Solution for 5x(3x-4)-3x(4x-2)=2x(5x+7) equation:

5x(3x-4)-3x(4x-2)=2x(5x+7)

We move all terms to the left:

5x(3x-4)-3x(4x-2)-(2x(5x+7))=0

We multiply parentheses

15x^2-12x^2-20x+6x-(2x(5x+7))=0


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

2x(5x+7)

We multiply parentheses

10x^2+14x

Back to the equation:

-(10x^2+14x)


We add all the numbers together, and all the variables

3x^2-14x-(10x^2+14x)=0

We get rid of parentheses

3x^2-10x^2-14x-14x=0

We add all the numbers together, and all the variables

-7x^2-28x=0

a = -7; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-7)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-7}=\frac{56}{-14}
=-4
$