7k^2+4k=3

Solution for 7k^2+4k=3 equation:

7k^2+4k=3

We move all terms to the left:

7k^2+4k-(3)=0

a = 7; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·7·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*7}=\frac{-14}{14}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*7}=\frac{6}{14}
=3/7
$