-4/10z+4/7z=10/9

Solution for -4/10z+4/7z=10/9 equation:

-4/10z+4/7z=10/9

We move all terms to the left:

-4/10z+4/7z-(10/9)=0


Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R



Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R


We add all the numbers together, and all the variables

-4/10z+4/7z-(+10/9)=0

We get rid of parentheses

-4/10z+4/7z-10/9=0

We calculate fractions


(-4900z^2)/5670z^2+(-2268z)/5670z^2+3240z/5670z^2=0

We multiply all the terms by the denominator


(-4900z^2)+(-2268z)+3240z=0

We add all the numbers together, and all the variables

(-4900z^2)+3240z+(-2268z)=0

We get rid of parentheses

-4900z^2+3240z-2268z=0

We add all the numbers together, and all the variables

-4900z^2+972z=0

a = -4900; b = 972; c = 0;
Δ = b2-4ac
Δ = 9722-4·(-4900)·0
Δ = 944784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{944784}=972$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(972)-972}{2*-4900}=\frac{-1944}{-9800}
=243/1225
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(972)+972}{2*-4900}=\frac{0}{-9800}
=0
$