5/8x+1=3x=69

Solution for 5/8x+1=3x=69 equation:

5/8x+1=3x=69

We move all terms to the left:

5/8x+1-(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+5/8x+1=0

We multiply all the terms by the denominator


-3x*8x+1*8x+5=0

Wy multiply elements

-24x^2+8x+5=0

a = -24; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-24)·5
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{34}}{2*-24}=\frac{-8-4\sqrt{34}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{34}}{2*-24}=\frac{-8+4\sqrt{34}}{-48}
$