27-11k2-7(k2-14)=0

Solution for 27-11k2-7(k2-14)=0 equation:

27-11k^2-7(k2-14)=0

We add all the numbers together, and all the variables

-11k^2-7(+k^2-14)+27=0

We multiply parentheses

-11k^2-7k^2+98+27=0

We add all the numbers together, and all the variables

-18k^2+125=0

a = -18; b = 0; c = +125;
Δ = b2-4ac
Δ = 02-4·(-18)·125
Δ = 9000
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:

$\sqrt{\Delta}=\sqrt{9000}=\sqrt{900*10}=\sqrt{900}*\sqrt{10}=30\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{10}}{2*-18}=\frac{0-30\sqrt{10}}{-36}
=-\frac{30\sqrt{10}}{-36}
=-\frac{5\sqrt{10}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{10}}{2*-18}=\frac{0+30\sqrt{10}}{-36}
=\frac{30\sqrt{10}}{-36}
=\frac{5\sqrt{10}}{-6}
$