k^2-76=-10k

Solution for k^2-76=-10k equation:

k^2-76=-10k

We move all terms to the left:

k^2-76-(-10k)=0

We get rid of parentheses

k^2+10k-76=0

a = 1; b = 10; c = -76;
Δ = b2-4ac
Δ = 102-4·1·(-76)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{101}}{2*1}=\frac{-10-2\sqrt{101}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{101}}{2*1}=\frac{-10+2\sqrt{101}}{2}
$