11-1/2a=3/4a+4

Solution for 11-1/2a=3/4a+4 equation:

11-1/2a=3/4a+4

We move all terms to the left:

11-1/2a-(3/4a+4)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a+4)!=0

a∈R


We get rid of parentheses

-1/2a-3/4a-4+11=0

We calculate fractions


(-4a)/8a^2+(-6a)/8a^2-4+11=0

We add all the numbers together, and all the variables

(-4a)/8a^2+(-6a)/8a^2+7=0

We multiply all the terms by the denominator


(-4a)+(-6a)+7*8a^2=0

Wy multiply elements

56a^2+(-4a)+(-6a)=0

We get rid of parentheses

56a^2-4a-6a=0

We add all the numbers together, and all the variables

56a^2-10a=0

a = 56; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·56·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*56}=\frac{0}{112}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*56}=\frac{20}{112}
=5/28
$