z^2+1=8+3z

Solution for z^2+1=8+3z equation:

z^2+1=8+3z

We move all terms to the left:

z^2+1-(8+3z)=0

We add all the numbers together, and all the variables

z^2-(3z+8)+1=0

We get rid of parentheses

z^2-3z-8+1=0

We add all the numbers together, and all the variables

z^2-3z-7=0

a = 1; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·1·(-7)
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{-(-3)-\sqrt{37}}{2*1}=\frac{3-\sqrt{37}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{37}}{2*1}=\frac{3+\sqrt{37}}{2}
$