3/(2-z)=2z+7

Solution for 3/(2-z)=2z+7 equation:

3/(2-z)=2z+7

We move all terms to the left:

3/(2-z)-(2z+7)=0


Domain of the equation: (2-z)!=0

We move all terms containing z to the left, all other terms to the right

-z!=-2

z!=-2/-1

z!=+2

z∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-2z*(-1z+2)-7*(-1z+2)+3=0

We multiply parentheses

2z^2-4z+7z-14+3=0

We add all the numbers together, and all the variables

2z^2+3z-11=0

a = 2; b = 3; c = -11;
Δ = b2-4ac
Δ = 32-4·2·(-11)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{97}}{2*2}=\frac{-3-\sqrt{97}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{97}}{2*2}=\frac{-3+\sqrt{97}}{4}
$