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

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

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

We move all terms to the left:

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


Domain of the equation: 10t!=0

t!=0/10

t!=0

t∈R



Domain of the equation: 5t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

100t^2-25t=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:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*100}=\frac{0}{200}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*100}=\frac{50}{200}
=1/4
$