2k^2+7=10k

Solution for 2k^2+7=10k equation:

2k^2+7=10k

We move all terms to the left:

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

a = 2; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·2·7
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{11}}{2*2}=\frac{10-2\sqrt{11}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{11}}{2*2}=\frac{10+2\sqrt{11}}{4}
$