-5/8a+7=21-18a

Solution for -5/8a+7=21-18a equation:

-5/8a+7=21-18a

We move all terms to the left:

-5/8a+7-(21-18a)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We add all the numbers together, and all the variables

-5/8a-(-18a+21)+7=0

We get rid of parentheses

-5/8a+18a-21+7=0

We multiply all the terms by the denominator


18a*8a-21*8a+7*8a-5=0

Wy multiply elements

144a^2-168a+56a-5=0

We add all the numbers together, and all the variables

144a^2-112a-5=0

a = 144; b = -112; c = -5;
Δ = b2-4ac
Δ = -1122-4·144·(-5)
Δ = 15424
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:

$\sqrt{\Delta}=\sqrt{15424}=\sqrt{64*241}=\sqrt{64}*\sqrt{241}=8\sqrt{241}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-8\sqrt{241}}{2*144}=\frac{112-8\sqrt{241}}{288}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+8\sqrt{241}}{2*144}=\frac{112+8\sqrt{241}}{288}
$