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

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

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

We move all terms to the left:

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


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

(x+8)2x

We multiply parentheses

2x^2+16x

Back to the equation:

-(2x^2+16x)


We get rid of parentheses

-2x^2+3x-16x-5=0

We add all the numbers together, and all the variables

-2x^2-13x-5=0

a = -2; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·(-2)·(-5)
Δ = 129
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{-(-13)-\sqrt{129}}{2*-2}=\frac{13-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{129}}{2*-2}=\frac{13+\sqrt{129}}{-4}
$