8k^2+35=47k

Solution for 8k^2+35=47k equation:

8k^2+35=47k

We move all terms to the left:

8k^2+35-(47k)=0

a = 8; b = -47; c = +35;
Δ = b2-4ac
Δ = -472-4·8·35
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-33}{2*8}=\frac{14}{16}
=7/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+33}{2*8}=\frac{80}{16}
=5
$