-1/4a+1=7+4.5a

Solution for -1/4a+1=7+4.5a equation:

-1/4a+1=7+4.5a

We move all terms to the left:

-1/4a+1-(7+4.5a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

-1/4a-(4.5a+7)+1=0

We get rid of parentheses

-1/4a-4.5a-7+1=0

We multiply all the terms by the denominator


-(4.5a)*4a-7*4a+1*4a-1=0

We add all the numbers together, and all the variables

-(+4.5a)*4a-7*4a+1*4a-1=0

We multiply parentheses

-16a^2-7*4a+1*4a-1=0

Wy multiply elements

-16a^2-28a+4a-1=0

We add all the numbers together, and all the variables

-16a^2-24a-1=0

a = -16; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-16)·(-1)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{2}}{2*-16}=\frac{24-16\sqrt{2}}{-32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{2}}{2*-16}=\frac{24+16\sqrt{2}}{-32}
$