x+21/2x+20=55

Solution for x+21/2x+20=55 equation:

x+21/2x+20=55

We move all terms to the left:

x+21/2x+20-(55)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+21/2x-35=0

We multiply all the terms by the denominator


x*2x-35*2x+21=0

Wy multiply elements

2x^2-70x+21=0

a = 2; b = -70; c = +21;
Δ = b2-4ac
Δ = -702-4·2·21
Δ = 4732
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:

$\sqrt{\Delta}=\sqrt{4732}=\sqrt{676*7}=\sqrt{676}*\sqrt{7}=26\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-26\sqrt{7}}{2*2}=\frac{70-26\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+26\sqrt{7}}{2*2}=\frac{70+26\sqrt{7}}{4}
$