3/4x-1.25=0.5x+4.5+1/4x

Solution for 3/4x-1.25=0.5x+4.5+1/4x equation:

3/4x-1.25=0.5x+4.5+1/4x

We move all terms to the left:

3/4x-1.25-(0.5x+4.5+1/4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(0.5x+1/4x+4.5)-1.25=0

We get rid of parentheses

3/4x-0.5x-1/4x-4.5-1.25=0

We multiply all the terms by the denominator


-(0.5x)*4x-(4.5)*4x-(1.25)*4x+3-1=0

We add all the numbers together, and all the variables

-(+0.5x)*4x-(4.5)*4x-(1.25)*4x+3-1=0

We add all the numbers together, and all the variables

-(+0.5x)*4x-(4.5)*4x-(1.25)*4x+2=0

We multiply parentheses

-0x^2-18x-5x+2=0

We add all the numbers together, and all the variables

-1x^2-23x+2=0

a = -1; b = -23; c = +2;
Δ = b2-4ac
Δ = -232-4·(-1)·2
Δ = 537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{537}}{2*-1}=\frac{23-\sqrt{537}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{537}}{2*-1}=\frac{23+\sqrt{537}}{-2}
$