2a-7/8a=1

Solution for 2a-7/8a=1 equation:

2a-7/8a=1

We move all terms to the left:

2a-7/8a-(1)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We multiply all the terms by the denominator


2a*8a-1*8a-7=0

Wy multiply elements

16a^2-8a-7=0

a = 16; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·16·(-7)
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{-(-8)-16\sqrt{2}}{2*16}=\frac{8-16\sqrt{2}}{32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{2}}{2*16}=\frac{8+16\sqrt{2}}{32}
$