1.4z-1=2/9z+9

Solution for 1.4z-1=2/9z+9 equation:

1.4z-1=2/9z+9

We move all terms to the left:

1.4z-1-(2/9z+9)=0


Domain of the equation: 9z+9)!=0

z∈R


We get rid of parentheses

1.4z-2/9z-9-1=0

We multiply all the terms by the denominator


(1.4z)*9z-9*9z-1*9z-2=0

We add all the numbers together, and all the variables

(+1.4z)*9z-9*9z-1*9z-2=0

We multiply parentheses

9z^2-9*9z-1*9z-2=0

Wy multiply elements

9z^2-81z-9z-2=0

We add all the numbers together, and all the variables

9z^2-90z-2=0

a = 9; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·9·(-2)
Δ = 8172
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:

$\sqrt{\Delta}=\sqrt{8172}=\sqrt{36*227}=\sqrt{36}*\sqrt{227}=6\sqrt{227}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{227}}{2*9}=\frac{90-6\sqrt{227}}{18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{227}}{2*9}=\frac{90+6\sqrt{227}}{18}
$