9z=61/2z-2

Solution for 9z=61/2z-2 equation:

9z=61/2z-2

We move all terms to the left:

9z-(61/2z-2)=0


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

z∈R


We get rid of parentheses

9z-61/2z+2=0

We multiply all the terms by the denominator


9z*2z+2*2z-61=0

Wy multiply elements

18z^2+4z-61=0

a = 18; b = 4; c = -61;
Δ = b2-4ac
Δ = 42-4·18·(-61)
Δ = 4408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4408}=\sqrt{4*1102}=\sqrt{4}*\sqrt{1102}=2\sqrt{1102}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{1102}}{2*18}=\frac{-4-2\sqrt{1102}}{36}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{1102}}{2*18}=\frac{-4+2\sqrt{1102}}{36}
$