2/5t-5/6=1/4t+3

Solution for 2/5t-5/6=1/4t+3 equation:

2/5t-5/6=1/4t+3

We move all terms to the left:

2/5t-5/6-(1/4t+3)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 4t+3)!=0

t∈R


We get rid of parentheses

2/5t-1/4t-3-5/6=0

We calculate fractions


(-400t^2)/720t^2+288t/720t^2+(-180t)/720t^2-3=0

We multiply all the terms by the denominator


(-400t^2)+288t+(-180t)-3*720t^2=0

Wy multiply elements

(-400t^2)-2160t^2+288t+(-180t)=0

We get rid of parentheses

-400t^2-2160t^2+288t-180t=0

We add all the numbers together, and all the variables

-2560t^2+108t=0

a = -2560; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-2560)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-2560}=\frac{-216}{-5120}
=27/640
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-2560}=\frac{0}{-5120}
=0
$