7/3-1/4z=7+2/5z

Solution for 7/3-1/4z=7+2/5z equation:

7/3-1/4z=7+2/5z

We move all terms to the left:

7/3-1/4z-(7+2/5z)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 5z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-1/4z-(2/5z+7)+7/3=0

We get rid of parentheses

-1/4z-2/5z-7+7/3=0

We calculate fractions


700z^2/180z^2+(-45z)/180z^2+(-72z)/180z^2-7=0

We multiply all the terms by the denominator


700z^2+(-45z)+(-72z)-7*180z^2=0

Wy multiply elements

700z^2-1260z^2+(-45z)+(-72z)=0

We get rid of parentheses

700z^2-1260z^2-45z-72z=0

We add all the numbers together, and all the variables

-560z^2-117z=0

a = -560; b = -117; c = 0;
Δ = b2-4ac
Δ = -1172-4·(-560)·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-117}{2*-560}=\frac{0}{-1120}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+117}{2*-560}=\frac{234}{-1120}
=-117/560
$