7/5z-3/10z=4

Solution for 7/5z-3/10z=4 equation:

7/5z-3/10z=4

We move all terms to the left:

7/5z-3/10z-(4)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R


We calculate fractions


70z/50z^2+(-15z)/50z^2-4=0

We multiply all the terms by the denominator


70z+(-15z)-4*50z^2=0

Wy multiply elements

-200z^2+70z+(-15z)=0

We get rid of parentheses

-200z^2+70z-15z=0

We add all the numbers together, and all the variables

-200z^2+55z=0

a = -200; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-200)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-200}=\frac{-110}{-400}
=11/40
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-200}=\frac{0}{-400}
=0
$