a+4/8a=3.75

Solution for a+4/8a=3.75 equation:

a+4/8a=3.75

We move all terms to the left:

a+4/8a-(3.75)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We add all the numbers together, and all the variables

a+4/8a-3.75=0

We multiply all the terms by the denominator


a*8a-(3.75)*8a+4=0

We multiply parentheses

a*8a-30a+4=0

Wy multiply elements

8a^2-30a+4=0

a = 8; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·8·4
Δ = 772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{193}}{2*8}=\frac{30-2\sqrt{193}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{193}}{2*8}=\frac{30+2\sqrt{193}}{16}
$