(89/10)-(33/10)j=-14-8

Solution for (89/10)-(33/10)j=-14-8 equation:

(89/10)-(33/10)j=-14-8

We move all terms to the left:

(89/10)-(33/10)j-(-14-8)=0


Domain of the equation: 10)j!=0

j!=0/1

j!=0

j∈R


We add all the numbers together, and all the variables

-(+33/10)j+(+89/10)-(-22)=0

We add all the numbers together, and all the variables

-(+33/10)j+22+(+89/10)=0

We multiply parentheses

-33j^2+22+(+89/10)=0

We get rid of parentheses

-33j^2+22+89/10=0

We multiply all the terms by the denominator


-33j^2*10+89+22*10=0

We add all the numbers together, and all the variables

-33j^2*10+309=0

Wy multiply elements

-330j^2+309=0

a = -330; b = 0; c = +309;
Δ = b2-4ac
Δ = 02-4·(-330)·309
Δ = 407880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{407880}=\sqrt{36*11330}=\sqrt{36}*\sqrt{11330}=6\sqrt{11330}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{11330}}{2*-330}=\frac{0-6\sqrt{11330}}{-660}
=-\frac{6\sqrt{11330}}{-660}
=-\frac{\sqrt{11330}}{-110}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{11330}}{2*-330}=\frac{0+6\sqrt{11330}}{-660}
=\frac{6\sqrt{11330}}{-660}
=\frac{\sqrt{11330}}{-110}
$