10.5=(x^2)/2x

Solution for 10.5=(x^2)/2x equation:

10.5=(x^2)/2x

We move all terms to the left:

10.5-((x^2)/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-x^2/2x+10.5=0

We multiply all the terms by the denominator


-x^2+(10.5)*2x=0

We add all the numbers together, and all the variables

-1x^2+(10.5)*2x=0

We multiply parentheses

-1x^2+21x=0

a = -1; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-1)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-1}=\frac{0}{-2}
=0
$