6/2t+4=-2/t-10

Solution for 6/2t+4=-2/t-10 equation:

6/2t+4=-2/t-10

We move all terms to the left:

6/2t+4-(-2/t-10)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: t-10)!=0

t∈R


We get rid of parentheses

6/2t+2/t+10+4=0

We calculate fractions


6t/2t^2+4t/2t^2+10+4=0

We add all the numbers together, and all the variables

6t/2t^2+4t/2t^2+14=0

We multiply all the terms by the denominator


6t+4t+14*2t^2=0

We add all the numbers together, and all the variables

10t+14*2t^2=0

Wy multiply elements

28t^2+10t=0

a = 28; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·28·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*28}=\frac{-20}{56}
=-5/14
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*28}=\frac{0}{56}
=0
$