88=8(k+5)k=

Solution for 88=8(k+5)k= equation:

88=8(k+5)k=

We move all terms to the left:

88-(8(k+5)k)=0


We calculate terms in parentheses: -(8(k+5)k), so:

8(k+5)k

We multiply parentheses

8k^2+40k

Back to the equation:

-(8k^2+40k)


We get rid of parentheses

-8k^2-40k+88=0

a = -8; b = -40; c = +88;
Δ = b2-4ac
Δ = -402-4·(-8)·88
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{69}}{2*-8}=\frac{40-8\sqrt{69}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{69}}{2*-8}=\frac{40+8\sqrt{69}}{-16}
$