6k2=-4k+10

Solution for 6k2=-4k+10 equation:

6k^2=-4k+10

We move all terms to the left:

6k^2-(-4k+10)=0

We get rid of parentheses

6k^2+4k-10=0

a = 6; b = 4; c = -10;
Δ = b2-4ac
Δ = 42-4·6·(-10)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*6}=\frac{-20}{12}
=-1+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*6}=\frac{12}{12}
=1
$