a=4/5a+7a-8

Solution for a=4/5a+7a-8 equation:

a=4/5a+7a-8

We move all terms to the left:

a-(4/5a+7a-8)=0


Domain of the equation: 5a+7a-8)!=0

a∈R


We add all the numbers together, and all the variables

a-(7a+4/5a-8)=0

We get rid of parentheses

a-7a-4/5a+8=0

We multiply all the terms by the denominator


a*5a-7a*5a+8*5a-4=0

Wy multiply elements

5a^2-35a^2+40a-4=0

We add all the numbers together, and all the variables

-30a^2+40a-4=0

a = -30; b = 40; c = -4;
Δ = b2-4ac
Δ = 402-4·(-30)·(-4)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{70}}{2*-30}=\frac{-40-4\sqrt{70}}{-60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{70}}{2*-30}=\frac{-40+4\sqrt{70}}{-60}
$