2x-1=3/4x+8

Solution for 2x-1=3/4x+8 equation:

2x-1=3/4x+8

We move all terms to the left:

2x-1-(3/4x+8)=0


Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

2x-3/4x-8-1=0

We multiply all the terms by the denominator


2x*4x-8*4x-1*4x-3=0

Wy multiply elements

8x^2-32x-4x-3=0

We add all the numbers together, and all the variables

8x^2-36x-3=0

a = 8; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·8·(-3)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{87}}{2*8}=\frac{36-4\sqrt{87}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{87}}{2*8}=\frac{36+4\sqrt{87}}{16}
$