1/12z+7/6z-5/8=15/4

Solution for 1/12z+7/6z-5/8=15/4 equation:

1/12z+7/6z-5/8=15/4

We move all terms to the left:

1/12z+7/6z-5/8-(15/4)=0


Domain of the equation: 12z!=0

z!=0/12

z!=0

z∈R



Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We add all the numbers together, and all the variables

1/12z+7/6z-5/8-(+15/4)=0

We get rid of parentheses

1/12z+7/6z-5/8-15/4=0

We calculate fractions


(-8640z^2)/18432z^2+(-51840z^2)/18432z^2+1536z/18432z^2+21504z/18432z^2=0

We multiply all the terms by the denominator


(-8640z^2)+(-51840z^2)+1536z+21504z=0

We add all the numbers together, and all the variables

(-8640z^2)+(-51840z^2)+23040z=0

We get rid of parentheses

-8640z^2-51840z^2+23040z=0

We add all the numbers together, and all the variables

-60480z^2+23040z=0

a = -60480; b = 23040; c = 0;
Δ = b2-4ac
Δ = 230402-4·(-60480)·0
Δ = 530841600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{530841600}=23040$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23040)-23040}{2*-60480}=\frac{-46080}{-120960}
=8/21
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23040)+23040}{2*-60480}=\frac{0}{-120960}
=0
$