35n^2+22n=-3

Solution for 35n^2+22n=-3 equation:

35n^2+22n=-3

We move all terms to the left:

35n^2+22n-(-3)=0

We add all the numbers together, and all the variables

35n^2+22n+3=0

a = 35; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·35·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8}{2*35}=\frac{-30}{70}
=-3/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8}{2*35}=\frac{-14}{70}
=-1/5
$