2t+8+1/2t=43

Solution for 2t+8+1/2t=43 equation:

2t+8+1/2t=43

We move all terms to the left:

2t+8+1/2t-(43)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

2t+1/2t-35=0

We multiply all the terms by the denominator


2t*2t-35*2t+1=0

Wy multiply elements

4t^2-70t+1=0

a = 4; b = -70; c = +1;
Δ = b2-4ac
Δ = -702-4·4·1
Δ = 4884
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:

$\sqrt{\Delta}=\sqrt{4884}=\sqrt{4*1221}=\sqrt{4}*\sqrt{1221}=2\sqrt{1221}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1221}}{2*4}=\frac{70-2\sqrt{1221}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1221}}{2*4}=\frac{70+2\sqrt{1221}}{8}
$