24.75-(3/8t)=t

Solution for 24.75-(3/8t)=t equation:

24.75-(3/8t)=t

We move all terms to the left:

24.75-(3/8t)-(t)=0


Domain of the equation: 8t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-(+3/8t)-t+24.75=0

We add all the numbers together, and all the variables

-1t-(+3/8t)+24.75=0

We get rid of parentheses

-1t-3/8t+24.75=0

We multiply all the terms by the denominator


-1t*8t+(24.75)*8t-3=0

We multiply parentheses

-1t*8t+198t-3=0

Wy multiply elements

-8t^2+198t-3=0

a = -8; b = 198; c = -3;
Δ = b2-4ac
Δ = 1982-4·(-8)·(-3)
Δ = 39108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{39108}=\sqrt{4*9777}=\sqrt{4}*\sqrt{9777}=2\sqrt{9777}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-2\sqrt{9777}}{2*-8}=\frac{-198-2\sqrt{9777}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+2\sqrt{9777}}{2*-8}=\frac{-198+2\sqrt{9777}}{-16}
$