(10=5z)2=5(z=4)

Solution for (10=5z)2=5(z=4) equation:

(10=5z)2=5(z=4)

We move all terms to the left:

(10-(5z)2)=0

We add all the numbers together, and all the variables

(-5z^2+10)=0

We get rid of parentheses

-5z^2+10=0

a = -5; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-5)·10
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-5}=\frac{0-10\sqrt{2}}{-10}
=-\frac{10\sqrt{2}}{-10}
=-\frac{\sqrt{2}}{-1}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-5}=\frac{0+10\sqrt{2}}{-10}
=\frac{10\sqrt{2}}{-10}
=\frac{\sqrt{2}}{-1}
$