14k^2-37k+2=-3

Solution for 14k^2-37k+2=-3 equation:

14k^2-37k+2=-3

We move all terms to the left:

14k^2-37k+2-(-3)=0

We add all the numbers together, and all the variables

14k^2-37k+5=0

a = 14; b = -37; c = +5;
Δ = b2-4ac
Δ = -372-4·14·5
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{-(-37)-33}{2*14}=\frac{4}{28}
=1/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+33}{2*14}=\frac{70}{28}
=2+1/2
$