1/2x+10=35-2x

Solution for 1/2x+10=35-2x equation:

1/2x+10=35-2x

We move all terms to the left:

1/2x+10-(35-2x)=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+35)+10=0

We get rid of parentheses

1/2x+2x-35+10=0

We multiply all the terms by the denominator


2x*2x-35*2x+10*2x+1=0

Wy multiply elements

4x^2-70x+20x+1=0

We add all the numbers together, and all the variables

4x^2-50x+1=0

a = 4; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·4·1
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{69}}{2*4}=\frac{50-6\sqrt{69}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{69}}{2*4}=\frac{50+6\sqrt{69}}{8}
$