4k^2=50-10k

Solution for 4k^2=50-10k equation:

4k^2=50-10k

We move all terms to the left:

4k^2-(50-10k)=0

We add all the numbers together, and all the variables

4k^2-(-10k+50)=0

We get rid of parentheses

4k^2+10k-50=0

a = 4; b = 10; c = -50;
Δ = b2-4ac
Δ = 102-4·4·(-50)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*4}=\frac{-40}{8}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*4}=\frac{20}{8}
=2+1/2
$