(i+5)*2i=26

Solution for (i+5)*2i=26 equation:

(i+5)*2i=26

We move all terms to the left:

(i+5)*2i-(26)=0

We multiply parentheses

2i^2+10i-26=0

a = 2; b = 10; c = -26;
Δ = b2-4ac
Δ = 102-4·2·(-26)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{77}}{2*2}=\frac{-10-2\sqrt{77}}{4}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{77}}{2*2}=\frac{-10+2\sqrt{77}}{4}
$