7/6z+7/10z-13/30=15/2

Solution for 7/6z+7/10z-13/30=15/2 equation:

7/6z+7/10z-13/30=15/2

We move all terms to the left:

7/6z+7/10z-13/30-(15/2)=0


Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R



Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R


We add all the numbers together, and all the variables

7/6z+7/10z-13/30-(+15/2)=0

We get rid of parentheses

7/6z+7/10z-13/30-15/2=0

We calculate fractions


(-1560z^2)/10800z^2+(-27000z^2)/10800z^2+12600z/10800z^2+7560z/10800z^2=0

We multiply all the terms by the denominator


(-1560z^2)+(-27000z^2)+12600z+7560z=0

We add all the numbers together, and all the variables

(-1560z^2)+(-27000z^2)+20160z=0

We get rid of parentheses

-1560z^2-27000z^2+20160z=0

We add all the numbers together, and all the variables

-28560z^2+20160z=0

a = -28560; b = 20160; c = 0;
Δ = b2-4ac
Δ = 201602-4·(-28560)·0
Δ = 406425600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{406425600}=20160$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20160)-20160}{2*-28560}=\frac{-40320}{-57120}
=12/17
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20160)+20160}{2*-28560}=\frac{0}{-57120}
=0
$