z+6=35z^2

Solution for z+6=35z^2 equation:

z+6=35z^2

We move all terms to the left:

z+6-(35z^2)=0

determiningTheFunctionDomain
-35z^2+z+6=0

a = -35; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-35)·6
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*-35}=\frac{-30}{-70}
=3/7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*-35}=\frac{28}{-70}
=-2/5
$