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

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

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

We move all terms to the left:

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


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

3x(8x+2)

We multiply parentheses

24x^2+6x

Back to the equation:

-(24x^2+6x)


We get rid of parentheses

-24x^2+5x-6x+2=0

We add all the numbers together, and all the variables

-24x^2-1x+2=0

a = -24; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-24)·2
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{193}}{2*-24}=\frac{1-\sqrt{193}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{193}}{2*-24}=\frac{1+\sqrt{193}}{-48}
$