-10=10k(k-8)

Solution for -10=10k(k-8) equation:

-10=10k(k-8)

We move all terms to the left:

-10-(10k(k-8))=0


We calculate terms in parentheses: -(10k(k-8)), so:

10k(k-8)

We multiply parentheses

10k^2-80k

Back to the equation:

-(10k^2-80k)


We get rid of parentheses

-10k^2+80k-10=0

a = -10; b = 80; c = -10;
Δ = b2-4ac
Δ = 802-4·(-10)·(-10)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{15}}{2*-10}=\frac{-80-20\sqrt{15}}{-20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{15}}{2*-10}=\frac{-80+20\sqrt{15}}{-20}
$