3(2x-1)+5=8x(x+1)

Solution for 3(2x-1)+5=8x(x+1) equation:

3(2x-1)+5=8x(x+1)

We move all terms to the left:

3(2x-1)+5-(8x(x+1))=0

We multiply parentheses

6x-(8x(x+1))-3+5=0


We calculate terms in parentheses: -(8x(x+1)), so:

8x(x+1)

We multiply parentheses

8x^2+8x

Back to the equation:

-(8x^2+8x)


We add all the numbers together, and all the variables

6x-(8x^2+8x)+2=0

We get rid of parentheses

-8x^2+6x-8x+2=0

We add all the numbers together, and all the variables

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

a = -8; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-8)·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{17}}{2*-8}=\frac{2-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{17}}{2*-8}=\frac{2+2\sqrt{17}}{-16}
$