2k2=30k-100

Solution for 2k2=30k-100 equation:

2k^2=30k-100

We move all terms to the left:

2k^2-(30k-100)=0

We get rid of parentheses

2k^2-30k+100=0

a = 2; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·2·100
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*2}=\frac{20}{4}
=5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*2}=\frac{40}{4}
=10
$