3i(2i-7)=6-21

Solution for 3i(2i-7)=6-21 equation:

3i(2i-7)=6-21

We move all terms to the left:

3i(2i-7)-(6-21)=0

We add all the numbers together, and all the variables

3i(2i-7)-(-15)=0

We add all the numbers together, and all the variables

3i(2i-7)+15=0

We multiply parentheses

6i^2-21i+15=0

a = 6; b = -21; c = +15;
Δ = b2-4ac
Δ = -212-4·6·15
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*6}=\frac{12}{12}
=1
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*6}=\frac{30}{12}
=2+1/2
$