3a-7=10(12)+1/4a

Solution for 3a-7=10(12)+1/4a equation:

3a-7=10(12)+1/4a

We move all terms to the left:

3a-7-(10(12)+1/4a)=0


Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3a-(1/4a+1012)-7=0

We get rid of parentheses

3a-1/4a-1012-7=0

We multiply all the terms by the denominator


3a*4a-1012*4a-7*4a-1=0

Wy multiply elements

12a^2-4048a-28a-1=0

We add all the numbers together, and all the variables

12a^2-4076a-1=0

a = 12; b = -4076; c = -1;
Δ = b2-4ac
Δ = -40762-4·12·(-1)
Δ = 16613824
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:

$\sqrt{\Delta}=\sqrt{16613824}=\sqrt{64*259591}=\sqrt{64}*\sqrt{259591}=8\sqrt{259591}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4076)-8\sqrt{259591}}{2*12}=\frac{4076-8\sqrt{259591}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4076)+8\sqrt{259591}}{2*12}=\frac{4076+8\sqrt{259591}}{24}
$