3/8x+5=3x

Solution for 3/8x+5=3x equation:

3/8x+5=3x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+3/8x+5=0

We multiply all the terms by the denominator


-3x*8x+5*8x+3=0

Wy multiply elements

-24x^2+40x+3=0

a = -24; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·(-24)·3
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{118}}{2*-24}=\frac{-40-4\sqrt{118}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{118}}{2*-24}=\frac{-40+4\sqrt{118}}{-48}
$