10-1/2t=3/4t+6

Solution for 10-1/2t=3/4t+6 equation:

10-1/2t=3/4t+6

We move all terms to the left:

10-1/2t-(3/4t+6)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t+6)!=0

t∈R


We get rid of parentheses

-1/2t-3/4t-6+10=0

We calculate fractions


(-4t)/8t^2+(-6t)/8t^2-6+10=0

We add all the numbers together, and all the variables

(-4t)/8t^2+(-6t)/8t^2+4=0

We multiply all the terms by the denominator


(-4t)+(-6t)+4*8t^2=0

Wy multiply elements

32t^2+(-4t)+(-6t)=0

We get rid of parentheses

32t^2-4t-6t=0

We add all the numbers together, and all the variables

32t^2-10t=0

a = 32; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·32·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*32}=\frac{0}{64}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*32}=\frac{20}{64}
=5/16
$