1/8a-7+7/8a-13-11a=0.75

Solution for 1/8a-7+7/8a-13-11a=0.75 equation:

1/8a-7+7/8a-13-11a=0.75

We move all terms to the left:

1/8a-7+7/8a-13-11a-(0.75)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We add all the numbers together, and all the variables

-11a+1/8a+7/8a-20.75=0

We multiply all the terms by the denominator


-11a*8a-(20.75)*8a+1+7=0

We add all the numbers together, and all the variables

-11a*8a-(20.75)*8a+8=0

We multiply parentheses

-11a*8a-166a+8=0

Wy multiply elements

-88a^2-166a+8=0

a = -88; b = -166; c = +8;
Δ = b2-4ac
Δ = -1662-4·(-88)·8
Δ = 30372
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:

$\sqrt{\Delta}=\sqrt{30372}=\sqrt{4*7593}=\sqrt{4}*\sqrt{7593}=2\sqrt{7593}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-2\sqrt{7593}}{2*-88}=\frac{166-2\sqrt{7593}}{-176}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+2\sqrt{7593}}{2*-88}=\frac{166+2\sqrt{7593}}{-176}
$