3+7z+z2=0

Solution for 3+7z+z2=0 equation:

3+7z+z2=0

We add all the numbers together, and all the variables

z^2+7z+3=0

a = 1; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·1·3
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{37}}{2*1}=\frac{-7-\sqrt{37}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{37}}{2*1}=\frac{-7+\sqrt{37}}{2}
$