1/2x+10=1.4x+54

Solution for 1/2x+10=1.4x+54 equation:

1/2x+10=1.4x+54

We move all terms to the left:

1/2x+10-(1.4x+54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-1.4x-54+10=0

We multiply all the terms by the denominator


-(1.4x)*2x-54*2x+10*2x+1=0

We add all the numbers together, and all the variables

-(+1.4x)*2x-54*2x+10*2x+1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·(-2)·1
Δ = 7752
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:

$\sqrt{\Delta}=\sqrt{7752}=\sqrt{4*1938}=\sqrt{4}*\sqrt{1938}=2\sqrt{1938}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1938}}{2*-2}=\frac{88-2\sqrt{1938}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1938}}{2*-2}=\frac{88+2\sqrt{1938}}{-4}
$