(7000-z2)/5000=0,25

Solution for (7000-z2)/5000=0,25 equation:

(7000-z2)/5000=0.25

We move all terms to the left:

(7000-z2)/5000-(0.25)=0

We add all the numbers together, and all the variables

(-1z^2+7000)/5000-(0.25)=0

We add all the numbers together, and all the variables

(-1z^2+7000)/5000-0.25=0

We multiply all the terms by the denominator


(-1z^2+7000)-(0.25)*5000=0

We add all the numbers together, and all the variables

(-1z^2+7000)-1250=0

We get rid of parentheses

-1z^2+7000-1250=0

We add all the numbers together, and all the variables

-1z^2+5750=0

a = -1; b = 0; c = +5750;
Δ = b2-4ac
Δ = 02-4·(-1)·5750
Δ = 23000
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:

$\sqrt{\Delta}=\sqrt{23000}=\sqrt{100*230}=\sqrt{100}*\sqrt{230}=10\sqrt{230}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{230}}{2*-1}=\frac{0-10\sqrt{230}}{-2}
=-\frac{10\sqrt{230}}{-2}
=-\frac{5\sqrt{230}}{-1}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{230}}{2*-1}=\frac{0+10\sqrt{230}}{-2}
=\frac{10\sqrt{230}}{-2}
=\frac{5\sqrt{230}}{-1}
$