8t-3/(t+1)=0

Solution for 8t-3/(t+1)=0 equation:

8t-3/(t+1)=0


Domain of the equation: (t+1)!=0

We move all terms containing t to the left, all other terms to the right

t!=-1

t∈R


We multiply all the terms by the denominator


8t*(t+1)-3=0

We multiply parentheses

8t^2+8t-3=0

a = 8; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·8·(-3)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*8}=\frac{-8-4\sqrt{10}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*8}=\frac{-8+4\sqrt{10}}{16}
$