42+18i-7i-3i2=0

Solution for 42+18i-7i-3i2=0 equation:

42+18i-7i-3i^2=0

We add all the numbers together, and all the variables

-3i^2+11i+42=0

a = -3; b = 11; c = +42;
Δ = b2-4ac
Δ = 112-4·(-3)·42
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*-3}=\frac{-36}{-6}
=+6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*-3}=\frac{14}{-6}
=-2+1/3
$