3z2=7z-1

Solution for 3z2=7z-1 equation:

3z^2=7z-1

We move all terms to the left:

3z^2-(7z-1)=0

We get rid of parentheses

3z^2-7z+1=0

a = 3; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·3·1
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*3}=\frac{7-\sqrt{37}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*3}=\frac{7+\sqrt{37}}{6}
$