50=3/2t-t

Solution for 50=3/2t-t equation:

50=3/2t-t

We move all terms to the left:

50-(3/2t-t)=0


Domain of the equation: 2t-t)!=0

t∈R


We add all the numbers together, and all the variables

-(-1t+3/2t)+50=0

We get rid of parentheses

1t-3/2t+50=0

We multiply all the terms by the denominator


1t*2t+50*2t-3=0

Wy multiply elements

2t^2+100t-3=0

a = 2; b = 100; c = -3;
Δ = b2-4ac
Δ = 1002-4·2·(-3)
Δ = 10024
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:

$\sqrt{\Delta}=\sqrt{10024}=\sqrt{4*2506}=\sqrt{4}*\sqrt{2506}=2\sqrt{2506}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2506}}{2*2}=\frac{-100-2\sqrt{2506}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2506}}{2*2}=\frac{-100+2\sqrt{2506}}{4}
$