2x=7/8x+3

Solution for 2x=7/8x+3 equation:

2x=7/8x+3

We move all terms to the left:

2x-(7/8x+3)=0


Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

2x-7/8x-3=0

We multiply all the terms by the denominator


2x*8x-3*8x-7=0

Wy multiply elements

16x^2-24x-7=0

a = 16; b = -24; c = -7;
Δ = b2-4ac
Δ = -242-4·16·(-7)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-32}{2*16}=\frac{-8}{32}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+32}{2*16}=\frac{56}{32}
=1+3/4
$