50+t=3/2t

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

50+t=3/2t

We move all terms to the left:

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


Domain of the equation: 2t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

t-3/2t+50=0

We multiply all the terms by the denominator


t*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}
$