k+4=25/k=29

Solution for k+4=25/k=29 equation:

k+4=25/k=29

We move all terms to the left:

k+4-(25/k)=0


Domain of the equation: k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

k-(+25/k)+4=0

We get rid of parentheses

k-25/k+4=0

We multiply all the terms by the denominator


k*k+4*k-25=0

We add all the numbers together, and all the variables

4k+k*k-25=0

Wy multiply elements

k^2+4k-25=0

a = 1; b = 4; c = -25;
Δ = b2-4ac
Δ = 42-4·1·(-25)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{29}}{2*1}=\frac{-4-2\sqrt{29}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{29}}{2*1}=\frac{-4+2\sqrt{29}}{2}
$