1/8t+3/5t-3=4

Solution for 1/8t+3/5t-3=4 equation:

1/8t+3/5t-3=4

We move all terms to the left:

1/8t+3/5t-3-(4)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R



Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We add all the numbers together, and all the variables

1/8t+3/5t-7=0

We calculate fractions


5t/40t^2+24t/40t^2-7=0

We multiply all the terms by the denominator


5t+24t-7*40t^2=0

We add all the numbers together, and all the variables

29t-7*40t^2=0

Wy multiply elements

-280t^2+29t=0

a = -280; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-280)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-280}=\frac{-58}{-560}
=29/280
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-280}=\frac{0}{-560}
=0
$