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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(4x(2x+7)), so:

4x(2x+7)

We multiply parentheses

8x^2+28x

Back to the equation:

-(8x^2+28x)


We get rid of parentheses

-8x^2+3x-28x=0

We add all the numbers together, and all the variables

-8x^2-25x=0

a = -8; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-8)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-8}=\frac{50}{-16}
=-3+1/8
$