1/4t-4=-6t+46

Solution for 1/4t-4=-6t+46 equation:

1/4t-4=-6t+46

We move all terms to the left:

1/4t-4-(-6t+46)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We get rid of parentheses

1/4t+6t-46-4=0

We multiply all the terms by the denominator


6t*4t-46*4t-4*4t+1=0

Wy multiply elements

24t^2-184t-16t+1=0

We add all the numbers together, and all the variables

24t^2-200t+1=0

a = 24; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·24·1
Δ = 39904
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:

$\sqrt{\Delta}=\sqrt{39904}=\sqrt{16*2494}=\sqrt{16}*\sqrt{2494}=4\sqrt{2494}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2494}}{2*24}=\frac{200-4\sqrt{2494}}{48}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2494}}{2*24}=\frac{200+4\sqrt{2494}}{48}
$