5x+21=2x(x+21)/2x

Solution for 5x+21=2x(x+21)/2x equation:

5x+21=2x(x+21)/2x

We move all terms to the left:

5x+21-(2x(x+21)/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x)-(2x(x+21)+21*2x)=0

Wy multiply elements

10x^2+42x=0

a = 10; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·10·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*10}=\frac{-84}{20}
=-4+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*10}=\frac{0}{20}
=0
$