(8i-14)(2i-6)=90

Solution for (8i-14)(2i-6)=90 equation:

(8i-14)(2i-6)=90

We move all terms to the left:

(8i-14)(2i-6)-(90)=0

We multiply parentheses ..

(+16i^2-48i-28i+84)-90=0

We get rid of parentheses

16i^2-48i-28i+84-90=0

We add all the numbers together, and all the variables

16i^2-76i-6=0

a = 16; b = -76; c = -6;
Δ = b2-4ac
Δ = -762-4·16·(-6)
Δ = 6160
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:

$\sqrt{\Delta}=\sqrt{6160}=\sqrt{16*385}=\sqrt{16}*\sqrt{385}=4\sqrt{385}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{385}}{2*16}=\frac{76-4\sqrt{385}}{32}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{385}}{2*16}=\frac{76+4\sqrt{385}}{32}
$