2x+1=5/4(x)

Solution for 2x+1=5/4(x) equation:

2x+1=5/4(x)

We move all terms to the left:

2x+1-(5/4(x))=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+5/4x)+1=0

We get rid of parentheses

2x-5/4x+1=0

We multiply all the terms by the denominator


2x*4x+1*4x-5=0

Wy multiply elements

8x^2+4x-5=0

a = 8; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·8·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*8}=\frac{-4-4\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*8}=\frac{-4+4\sqrt{11}}{16}
$