1/2a+3.75=a

Solution for 1/2a+3.75=a equation:

1/2a+3.75=a

We move all terms to the left:

1/2a+3.75-(a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/2a+3.75=0

We multiply all the terms by the denominator


-1a*2a+(3.75)*2a+1=0

We multiply parentheses

-1a*2a+7.5a+1=0

Wy multiply elements

-2a^2+7.5a+1=0

a = -2; b = 7.5; c = +1;
Δ = b2-4ac
Δ = 7.52-4·(-2)·1
Δ = 64.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7.5)-\sqrt{64.25}}{2*-2}=\frac{-7.5-\sqrt{64.25}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{64.25}}{2*-2}=\frac{-7.5+\sqrt{64.25}}{-4}
$