(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!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

(8a-24)(a-3)/5a-167=0

We multiply parentheses ..

(+8a^2-24a-24a+72)/5a-167=0

We multiply all the terms by the denominator


(+8a^2-24a-24a+72)-167*5a=0

Wy multiply elements

(+8a^2-24a-24a+72)-835a=0

We get rid of parentheses

8a^2-24a-24a-835a+72=0

We add all the numbers together, and all the variables

8a^2-883a+72=0

a = 8; b = -883; c = +72;
Δ = b2-4ac
Δ = -8832-4·8·72
Δ = 777385
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:

$\sqrt{\Delta}=\sqrt{777385}=\sqrt{49*15865}=\sqrt{49}*\sqrt{15865}=7\sqrt{15865}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-883)-7\sqrt{15865}}{2*8}=\frac{883-7\sqrt{15865}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-883)+7\sqrt{15865}}{2*8}=\frac{883+7\sqrt{15865}}{16}
$