2(7/16a+5)=7/8a

Solution for 2(7/16a+5)=7/8a equation:

2(7/16a+5)=7/8a

We move all terms to the left:

2(7/16a+5)-(7/8a)=0


Domain of the equation: 16a+5)!=0

a∈R



Domain of the equation: 8a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2(7/16a+5)-(+7/8a)=0

We multiply parentheses

14a-(+7/8a)+10=0

We get rid of parentheses

14a-7/8a+10=0

We multiply all the terms by the denominator


14a*8a+10*8a-7=0

Wy multiply elements

112a^2+80a-7=0

a = 112; b = 80; c = -7;
Δ = b2-4ac
Δ = 802-4·112·(-7)
Δ = 9536
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:

$\sqrt{\Delta}=\sqrt{9536}=\sqrt{64*149}=\sqrt{64}*\sqrt{149}=8\sqrt{149}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{149}}{2*112}=\frac{-80-8\sqrt{149}}{224}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{149}}{2*112}=\frac{-80+8\sqrt{149}}{224}
$