-8/5a+32=4a-38

Solution for -8/5a+32=4a-38 equation:

-8/5a+32=4a-38

We move all terms to the left:

-8/5a+32-(4a-38)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

-8/5a-4a+38+32=0

We multiply all the terms by the denominator


-4a*5a+38*5a+32*5a-8=0

Wy multiply elements

-20a^2+190a+160a-8=0

We add all the numbers together, and all the variables

-20a^2+350a-8=0

a = -20; b = 350; c = -8;
Δ = b2-4ac
Δ = 3502-4·(-20)·(-8)
Δ = 121860
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:

$\sqrt{\Delta}=\sqrt{121860}=\sqrt{36*3385}=\sqrt{36}*\sqrt{3385}=6\sqrt{3385}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(350)-6\sqrt{3385}}{2*-20}=\frac{-350-6\sqrt{3385}}{-40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(350)+6\sqrt{3385}}{2*-20}=\frac{-350+6\sqrt{3385}}{-40}
$