10x^2/(x+8)=40

Solution for 10x^2/(x+8)=40 equation:

10x^2/(x+8)=40

We move all terms to the left:

10x^2/(x+8)-(40)=0


Domain of the equation: (x+8)!=0

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

x!=-8

x∈R


We multiply all the terms by the denominator


10x^2-40*(x+8)=0

We multiply parentheses

10x^2-40x-320=0

a = 10; b = -40; c = -320;
Δ = b2-4ac
Δ = -402-4·10·(-320)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-120}{2*10}=\frac{-80}{20}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+120}{2*10}=\frac{160}{20}
=8
$