18+.5x=1/4x+54

Solution for 18+.5x=1/4x+54 equation:

18+.5x=1/4x+54

We move all terms to the left:

18+.5x-(1/4x+54)=0


Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

.5x-1/4x-54+18=0

We multiply all the terms by the denominator


(.5x)*4x-54*4x+18*4x-1=0

We add all the numbers together, and all the variables

(+.5x)*4x-54*4x+18*4x-1=0

We multiply parentheses

4x^2-54*4x+18*4x-1=0

Wy multiply elements

4x^2-216x+72x-1=0

We add all the numbers together, and all the variables

4x^2-144x-1=0

a = 4; b = -144; c = -1;
Δ = b2-4ac
Δ = -1442-4·4·(-1)
Δ = 20752
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:

$\sqrt{\Delta}=\sqrt{20752}=\sqrt{16*1297}=\sqrt{16}*\sqrt{1297}=4\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1297}}{2*4}=\frac{144-4\sqrt{1297}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1297}}{2*4}=\frac{144+4\sqrt{1297}}{8}
$