4(1/8t+2)=2(t-8)-1/2t

Solution for 4(1/8t+2)=2(t-8)-1/2t equation:

4(1/8t+2)=2(t-8)-1/2t

We move all terms to the left:

4(1/8t+2)-(2(t-8)-1/2t)=0


Domain of the equation: 8t+2)!=0

t∈R



Domain of the equation: 2t)!=0

t!=0/1

t!=0

t∈R


We multiply parentheses

4t-(2(t-8)-1/2t)+8=0

We multiply all the terms by the denominator


4t*2t)-(2(t-8)+8*2t)-1=0

Wy multiply elements

8t^2+16t=0

a = 8; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·8·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*8}=\frac{-32}{16}
=-2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*8}=\frac{0}{16}
=0
$