5k^2=-7k+90

Solution for 5k^2=-7k+90 equation:

5k^2=-7k+90

We move all terms to the left:

5k^2-(-7k+90)=0

We get rid of parentheses

5k^2+7k-90=0

a = 5; b = 7; c = -90;
Δ = b2-4ac
Δ = 72-4·5·(-90)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-43}{2*5}=\frac{-50}{10}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+43}{2*5}=\frac{36}{10}
=3+3/5
$