4k2-14=-14+10k

Solution for 4k2-14=-14+10k equation:

4k^2-14=-14+10k

We move all terms to the left:

4k^2-14-(-14+10k)=0

We add all the numbers together, and all the variables

4k^2-(10k-14)-14=0

We get rid of parentheses

4k^2-10k+14-14=0

We add all the numbers together, and all the variables

4k^2-10k=0

a = 4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·4·0
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{-(-10)-10}{2*4}=\frac{0}{8}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*4}=\frac{20}{8}
=2+1/2
$