2t-1=3/4t+9

Solution for 2t-1=3/4t+9 equation:

2t-1=3/4t+9

We move all terms to the left:

2t-1-(3/4t+9)=0


Domain of the equation: 4t+9)!=0

t∈R


We get rid of parentheses

2t-3/4t-9-1=0

We multiply all the terms by the denominator


2t*4t-9*4t-1*4t-3=0

Wy multiply elements

8t^2-36t-4t-3=0

We add all the numbers together, and all the variables

8t^2-40t-3=0

a = 8; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·8·(-3)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*8}=\frac{40-4\sqrt{106}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*8}=\frac{40+4\sqrt{106}}{16}
$