27/16a+5=7/8a-10

Solution for 27/16a+5=7/8a-10 equation:

27/16a+5=7/8a-10

We move all terms to the left:

27/16a+5-(7/8a-10)=0


Domain of the equation: 16a!=0

a!=0/16

a!=0

a∈R



Domain of the equation: 8a-10)!=0

a∈R


We get rid of parentheses

27/16a-7/8a+10+5=0

We calculate fractions


216a/128a^2+(-112a)/128a^2+10+5=0

We add all the numbers together, and all the variables

216a/128a^2+(-112a)/128a^2+15=0

We multiply all the terms by the denominator


216a+(-112a)+15*128a^2=0

Wy multiply elements

1920a^2+216a+(-112a)=0

We get rid of parentheses

1920a^2+216a-112a=0

We add all the numbers together, and all the variables

1920a^2+104a=0

a = 1920; b = 104; c = 0;
Δ = b2-4ac
Δ = 1042-4·1920·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-104}{2*1920}=\frac{-208}{3840}
=-13/240
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+104}{2*1920}=\frac{0}{3840}
=0
$