50z^2=36-5z

Solution for 50z^2=36-5z equation:

50z^2=36-5z

We move all terms to the left:

50z^2-(36-5z)=0

We add all the numbers together, and all the variables

50z^2-(-5z+36)=0

We get rid of parentheses

50z^2+5z-36=0

a = 50; b = 5; c = -36;
Δ = b2-4ac
Δ = 52-4·50·(-36)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-85}{2*50}=\frac{-90}{100}
=-9/10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+85}{2*50}=\frac{80}{100}
=4/5
$