4x+2=2(2x-3)8x-1=6x+32x+3=2x+3

Solution for 4x+2=2(2x-3)8x-1=6x+32x+3=2x+3 equation:

4x+2=2(2x-3)8x-1=6x+32x+3=2x+3

We move all terms to the left:

4x+2-(2(2x-3)8x-1)=0


We calculate terms in parentheses: -(2(2x-3)8x-1), so:

2(2x-3)8x-1

We multiply parentheses

32x^2-48x-1

Back to the equation:

-(32x^2-48x-1)


We get rid of parentheses

-32x^2+4x+48x+1+2=0

We add all the numbers together, and all the variables

-32x^2+52x+3=0

a = -32; b = 52; c = +3;
Δ = b2-4ac
Δ = 522-4·(-32)·3
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{193}}{2*-32}=\frac{-52-4\sqrt{193}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{193}}{2*-32}=\frac{-52+4\sqrt{193}}{-64}
$