4k^2+4k=35

Solution for 4k^2+4k=35 equation:

4k^2+4k=35

We move all terms to the left:

4k^2+4k-(35)=0

a = 4; b = 4; c = -35;
Δ = b2-4ac
Δ = 42-4·4·(-35)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-24}{2*4}=\frac{-28}{8}
=-3+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+24}{2*4}=\frac{20}{8}
=2+1/2
$