12a-28/4a=1

Solution for 12a-28/4a=1 equation:

12a-28/4a=1

We move all terms to the left:

12a-28/4a-(1)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We multiply all the terms by the denominator


12a*4a-1*4a-28=0

Wy multiply elements

48a^2-4a-28=0

a = 48; b = -4; c = -28;
Δ = b2-4ac
Δ = -42-4·48·(-28)
Δ = 5392
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:

$\sqrt{\Delta}=\sqrt{5392}=\sqrt{16*337}=\sqrt{16}*\sqrt{337}=4\sqrt{337}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{337}}{2*48}=\frac{4-4\sqrt{337}}{96}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{337}}{2*48}=\frac{4+4\sqrt{337}}{96}
$