-2i2+7i=-2-7i

Solution for -2i2+7i=-2-7i equation:

-2i^2+7i=-2-7i

We move all terms to the left:

-2i^2+7i-(-2-7i)=0

We add all the numbers together, and all the variables

-2i^2+7i-(-7i-2)=0

We get rid of parentheses

-2i^2+7i+7i+2=0

We add all the numbers together, and all the variables

-2i^2+14i+2=0

a = -2; b = 14; c = +2;
Δ = b2-4ac
Δ = 142-4·(-2)·2
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*-2}=\frac{-14-2\sqrt{53}}{-4}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*-2}=\frac{-14+2\sqrt{53}}{-4}
$