7+1/2x=50-2x

Solution for 7+1/2x=50-2x equation:

7+1/2x=50-2x

We move all terms to the left:

7+1/2x-(50-2x)=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+50)+7=0

We get rid of parentheses

1/2x+2x-50+7=0

We multiply all the terms by the denominator


2x*2x-50*2x+7*2x+1=0

Wy multiply elements

4x^2-100x+14x+1=0

We add all the numbers together, and all the variables

4x^2-86x+1=0

a = 4; b = -86; c = +1;
Δ = b2-4ac
Δ = -862-4·4·1
Δ = 7380
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:

$\sqrt{\Delta}=\sqrt{7380}=\sqrt{36*205}=\sqrt{36}*\sqrt{205}=6\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-6\sqrt{205}}{2*4}=\frac{86-6\sqrt{205}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+6\sqrt{205}}{2*4}=\frac{86+6\sqrt{205}}{8}
$