(-1+9i)(i)+(3+3i)=(9-6i)

Solution for (-1+9i)(i)+(3+3i)=(9-6i) equation:

(-1+9i)(i)+(3+3i)=(9-6i)

We move all terms to the left:

(-1+9i)(i)+(3+3i)-((9-6i))=0

We add all the numbers together, and all the variables

(9i-1)i+(3i+3)-((-6i+9))=0

We multiply parentheses

9i^2-1i+(3i+3)-((-6i+9))=0

We get rid of parentheses

9i^2-1i+3i-((-6i+9))+3=0


We calculate terms in parentheses: -((-6i+9)), so:

(-6i+9)

We get rid of parentheses

-6i+9

Back to the equation:

-(-6i+9)


We add all the numbers together, and all the variables

9i^2+2i-(-6i+9)+3=0

We get rid of parentheses

9i^2+2i+6i-9+3=0

We add all the numbers together, and all the variables

9i^2+8i-6=0

a = 9; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·9·(-6)
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{70}}{2*9}=\frac{-8-2\sqrt{70}}{18}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{70}}{2*9}=\frac{-8+2\sqrt{70}}{18}
$