10t=3/4(t)

Solution for 10t=3/4(t) equation:

10t=3/4(t)

We move all terms to the left:

10t-(3/4(t))=0


Domain of the equation: 4t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

10t-(+3/4t)=0

We get rid of parentheses

10t-3/4t=0

We multiply all the terms by the denominator


10t*4t-3=0

Wy multiply elements

40t^2-3=0

a = 40; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·40·(-3)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*40}=\frac{0-4\sqrt{30}}{80}
=-\frac{4\sqrt{30}}{80}
=-\frac{\sqrt{30}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*40}=\frac{0+4\sqrt{30}}{80}
=\frac{4\sqrt{30}}{80}
=\frac{\sqrt{30}}{20}
$