5k+9=10(1/2*k+1)

Solution for 5k+9=10(1/2*k+1) equation:

5k+9=10(1/2k+1)

We move all terms to the left:

5k+9-(10(1/2k+1))=0


Domain of the equation: 2k+1))!=0

k∈R


We multiply all the terms by the denominator


5k*2k+9*2k+1))-(10(1+1))=0

We add all the numbers together, and all the variables

5k*2k+9*2k+1))-(102)=0

We add all the numbers together, and all the variables

5k*2k+9*2k=0

Wy multiply elements

10k^2+18k=0

a = 10; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·10·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*10}=\frac{-36}{20}
=-1+4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*10}=\frac{0}{20}
=0
$