1250=80t+1/2(4)t

Solution for 1250=80t+1/2(4)t equation:

1250=80t+1/2(4)t

We move all terms to the left:

1250-(80t+1/2(4)t)=0


Domain of the equation: 24t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-(+80t+1/24t)+1250=0

We get rid of parentheses

-80t-1/24t+1250=0

We multiply all the terms by the denominator


-80t*24t+1250*24t-1=0

Wy multiply elements

-1920t^2+30000t-1=0

a = -1920; b = 30000; c = -1;
Δ = b2-4ac
Δ = 300002-4·(-1920)·(-1)
Δ = 899992320
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:

$\sqrt{\Delta}=\sqrt{899992320}=\sqrt{256*3515595}=\sqrt{256}*\sqrt{3515595}=16\sqrt{3515595}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30000)-16\sqrt{3515595}}{2*-1920}=\frac{-30000-16\sqrt{3515595}}{-3840}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30000)+16\sqrt{3515595}}{2*-1920}=\frac{-30000+16\sqrt{3515595}}{-3840}
$