1/4x+18=1.5x+3.75

Solution for 1/4x+18=1.5x+3.75 equation:

1/4x+18=1.5x+3.75

We move all terms to the left:

1/4x+18-(1.5x+3.75)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-1.5x-3.75+18=0

We multiply all the terms by the denominator


-(1.5x)*4x-(3.75)*4x+18*4x+1=0

We add all the numbers together, and all the variables

-(+1.5x)*4x-(3.75)*4x+18*4x+1=0

We multiply parentheses

-4x^2-15x+18*4x+1=0

Wy multiply elements

-4x^2-15x+72x+1=0

We add all the numbers together, and all the variables

-4x^2+57x+1=0

a = -4; b = 57; c = +1;
Δ = b2-4ac
Δ = 572-4·(-4)·1
Δ = 3265
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{-(57)-\sqrt{3265}}{2*-4}=\frac{-57-\sqrt{3265}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{3265}}{2*-4}=\frac{-57+\sqrt{3265}}{-8}
$