(w-2)(48/w+3)=70

Solution for (w-2)(48/w+3)=70 equation:

(w-2)(48/w+3)=70

We move all terms to the left:

(w-2)(48/w+3)-(70)=0


Domain of the equation: w+3)!=0

w∈R


We multiply parentheses ..

(+48w^2+3w-96w-6)-70=0

We get rid of parentheses

48w^2+3w-96w-6-70=0

We add all the numbers together, and all the variables

48w^2-93w-76=0

a = 48; b = -93; c = -76;
Δ = b2-4ac
Δ = -932-4·48·(-76)
Δ = 23241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-\sqrt{23241}}{2*48}=\frac{93-\sqrt{23241}}{96}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+\sqrt{23241}}{2*48}=\frac{93+\sqrt{23241}}{96}
$