95-3/4z=4z

Solution for 95-3/4z=4z equation:

95-3/4z=4z

We move all terms to the left:

95-3/4z-(4z)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R


We add all the numbers together, and all the variables

-4z-3/4z+95=0

We multiply all the terms by the denominator


-4z*4z+95*4z-3=0

Wy multiply elements

-16z^2+380z-3=0

a = -16; b = 380; c = -3;
Δ = b2-4ac
Δ = 3802-4·(-16)·(-3)
Δ = 144208
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:

$\sqrt{\Delta}=\sqrt{144208}=\sqrt{16*9013}=\sqrt{16}*\sqrt{9013}=4\sqrt{9013}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-4\sqrt{9013}}{2*-16}=\frac{-380-4\sqrt{9013}}{-32}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+4\sqrt{9013}}{2*-16}=\frac{-380+4\sqrt{9013}}{-32}
$