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 add all the numbers together, and all the variables

1/2x-(-4x+55)+10=0

We get rid of parentheses

1/2x+4x-55+10=0

We multiply all the terms by the denominator


4x*2x-55*2x+10*2x+1=0

Wy multiply elements

8x^2-110x+20x+1=0

We add all the numbers together, and all the variables

8x^2-90x+1=0

a = 8; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·8·1
Δ = 8068
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:

$\sqrt{\Delta}=\sqrt{8068}=\sqrt{4*2017}=\sqrt{4}*\sqrt{2017}=2\sqrt{2017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2017}}{2*8}=\frac{90-2\sqrt{2017}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2017}}{2*8}=\frac{90+2\sqrt{2017}}{16}
$