98=z(z-84)

Solution for 98=z(z-84) equation:

98=z(z-84)

We move all terms to the left:

98-(z(z-84))=0


We calculate terms in parentheses: -(z(z-84)), so:

z(z-84)

We multiply parentheses

z^2-84z

Back to the equation:

-(z^2-84z)


We get rid of parentheses

-z^2+84z+98=0

We add all the numbers together, and all the variables

-1z^2+84z+98=0

a = -1; b = 84; c = +98;
Δ = b2-4ac
Δ = 842-4·(-1)·98
Δ = 7448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7448}=\sqrt{196*38}=\sqrt{196}*\sqrt{38}=14\sqrt{38}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-14\sqrt{38}}{2*-1}=\frac{-84-14\sqrt{38}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+14\sqrt{38}}{2*-1}=\frac{-84+14\sqrt{38}}{-2}
$