3k^2-10k=-7

Solution for 3k^2-10k=-7 equation:

3k^2-10k=-7

We move all terms to the left:

3k^2-10k-(-7)=0

We add all the numbers together, and all the variables

3k^2-10k+7=0

a = 3; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·3·7
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*3}=\frac{6}{6}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*3}=\frac{14}{6}
=2+1/3
$