x+21/2x+10=52

Solution for x+21/2x+10=52 equation:

x+21/2x+10=52

We move all terms to the left:

x+21/2x+10-(52)=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-42=0

We multiply all the terms by the denominator


x*2x-42*2x+21=0

Wy multiply elements

2x^2-84x+21=0

a = 2; b = -84; c = +21;
Δ = b2-4ac
Δ = -842-4·2·21
Δ = 6888
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:

$\sqrt{\Delta}=\sqrt{6888}=\sqrt{4*1722}=\sqrt{4}*\sqrt{1722}=2\sqrt{1722}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1722}}{2*2}=\frac{84-2\sqrt{1722}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1722}}{2*2}=\frac{84+2\sqrt{1722}}{4}
$