8-7/10i=6-1/5i

Solution for 8-7/10i=6-1/5i equation:

8-7/10i=6-1/5i

We move all terms to the left:

8-7/10i-(6-1/5i)=0


Domain of the equation: 10i!=0

i!=0/10

i!=0

i∈R



Domain of the equation: 5i)!=0

i!=0/1

i!=0

i∈R


We add all the numbers together, and all the variables

-7/10i-(-1/5i+6)+8=0

We get rid of parentheses

-7/10i+1/5i-6+8=0

We calculate fractions


(-35i)/50i^2+10i/50i^2-6+8=0

We add all the numbers together, and all the variables

(-35i)/50i^2+10i/50i^2+2=0

We multiply all the terms by the denominator


(-35i)+10i+2*50i^2=0

We add all the numbers together, and all the variables

10i+(-35i)+2*50i^2=0

Wy multiply elements

100i^2+10i+(-35i)=0

We get rid of parentheses

100i^2+10i-35i=0

We add all the numbers together, and all the variables

100i^2-25i=0

a = 100; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·100·0
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{-(-25)-25}{2*100}=\frac{0}{200}
=0
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*100}=\frac{50}{200}
=1/4
$