3/5z+1.2=z

Solution for 3/5z+1.2=z equation:

3/5z+1.2=z

We move all terms to the left:

3/5z+1.2-(z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We add all the numbers together, and all the variables

-1z+3/5z+1.2=0

We multiply all the terms by the denominator


-1z*5z+(1.2)*5z+3=0

We multiply parentheses

-1z*5z+6z+3=0

Wy multiply elements

-5z^2+6z+3=0

a = -5; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-5)·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*-5}=\frac{-6-4\sqrt{6}}{-10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*-5}=\frac{-6+4\sqrt{6}}{-10}
$