7+1/2x=57-2x

Solution for 7+1/2x=57-2x equation:

7+1/2x=57-2x

We move all terms to the left:

7+1/2x-(57-2x)=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-(-2x+57)+7=0

We get rid of parentheses

1/2x+2x-57+7=0

We multiply all the terms by the denominator


2x*2x-57*2x+7*2x+1=0

Wy multiply elements

4x^2-114x+14x+1=0

We add all the numbers together, and all the variables

4x^2-100x+1=0

a = 4; b = -100; c = +1;
Δ = b2-4ac
Δ = -1002-4·4·1
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-16\sqrt{39}}{2*4}=\frac{100-16\sqrt{39}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+16\sqrt{39}}{2*4}=\frac{100+16\sqrt{39}}{8}
$