24/y+y=10

Solution for 24/y+y=10 equation:

24/y+y=10

We move all terms to the left:

24/y+y-(10)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+24/y-10=0

We multiply all the terms by the denominator


y*y-10*y+24=0

We add all the numbers together, and all the variables

-10y+y*y+24=0

Wy multiply elements

y^2-10y+24=0

a = 1; b = -10; c = +24;
Δ = b2-4ac
Δ = -102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*1}=\frac{8}{2}
=4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*1}=\frac{12}{2}
=6
$