63z=49+8z^2

Solution for 63z=49+8z^2 equation:

63z=49+8z^2

We move all terms to the left:

63z-(49+8z^2)=0

We get rid of parentheses

-8z^2+63z-49=0

a = -8; b = 63; c = -49;
Δ = b2-4ac
Δ = 632-4·(-8)·(-49)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-49}{2*-8}=\frac{-112}{-16}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+49}{2*-8}=\frac{-14}{-16}
=7/8
$