1/2x+10=0.25x+54

Solution for 1/2x+10=0.25x+54 equation:

1/2x+10=0.25x+54

We move all terms to the left:

1/2x+10-(0.25x+54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-0.25x-54+10=0

We multiply all the terms by the denominator


-(0.25x)*2x-54*2x+10*2x+1=0

We add all the numbers together, and all the variables

-(+0.25x)*2x-54*2x+10*2x+1=0

We multiply parentheses

-0x^2-54*2x+10*2x+1=0

Wy multiply elements

-0x^2-108x+20x+1=0

We add all the numbers together, and all the variables

-1x^2-88x+1=0

a = -1; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·(-1)·1
Δ = 7748
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:

$\sqrt{\Delta}=\sqrt{7748}=\sqrt{4*1937}=\sqrt{4}*\sqrt{1937}=2\sqrt{1937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1937}}{2*-1}=\frac{88-2\sqrt{1937}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1937}}{2*-1}=\frac{88+2\sqrt{1937}}{-2}
$