3x(2x-4)+5x+7=5x(4x+1)+4x-3

Solution for 3x(2x-4)+5x+7=5x(4x+1)+4x-3 equation:

3x(2x-4)+5x+7=5x(4x+1)+4x-3

We move all terms to the left:

3x(2x-4)+5x+7-(5x(4x+1)+4x-3)=0

We add all the numbers together, and all the variables

5x+3x(2x-4)-(5x(4x+1)+4x-3)+7=0

We multiply parentheses

6x^2+5x-12x-(5x(4x+1)+4x-3)+7=0


We calculate terms in parentheses: -(5x(4x+1)+4x-3), so:

5x(4x+1)+4x-3

We add all the numbers together, and all the variables

4x+5x(4x+1)-3

We multiply parentheses

20x^2+4x+5x-3

We add all the numbers together, and all the variables

20x^2+9x-3

Back to the equation:

-(20x^2+9x-3)


We add all the numbers together, and all the variables

6x^2-7x-(20x^2+9x-3)+7=0

We get rid of parentheses

6x^2-20x^2-7x-9x+3+7=0

We add all the numbers together, and all the variables

-14x^2-16x+10=0

a = -14; b = -16; c = +10;
Δ = b2-4ac
Δ = -162-4·(-14)·10
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{51}}{2*-14}=\frac{16-4\sqrt{51}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{51}}{2*-14}=\frac{16+4\sqrt{51}}{-28}
$