(8a*24)(a-3)/(5a-15)=152

Solution for (8a*24)(a-3)/(5a-15)=152 equation:

(8a*24)(a-3)/(5a-15)=152

We move all terms to the left:

(8a*24)(a-3)/(5a-15)-(152)=0


Domain of the equation: (5a-15)!=0

We move all terms containing a to the left, all other terms to the right

5a!=15

a!=15/5

a!=3

a∈R


We add all the numbers together, and all the variables

(+8a*24)(a-3)/(5a-15)-152=0

We multiply parentheses ..

(+192a^2-576a)/(5a-15)-152=0

We multiply all the terms by the denominator


(+192a^2-576a)-152*(5a-15)=0

We multiply parentheses

(+192a^2-576a)-760a+2280=0

We get rid of parentheses

192a^2-576a-760a+2280=0

We add all the numbers together, and all the variables

192a^2-1336a+2280=0

a = 192; b = -1336; c = +2280;
Δ = b2-4ac
Δ = -13362-4·192·2280
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1336)-184}{2*192}=\frac{1152}{384}
=3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1336)+184}{2*192}=\frac{1520}{384}
=3+23/24
$