96/x+10=4x-10

Solution for 96/x+10=4x-10 equation:

96/x+10=4x-10

We move all terms to the left:

96/x+10-(4x-10)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

96/x-4x+10+10=0

We multiply all the terms by the denominator


-4x*x+10*x+10*x+96=0

We add all the numbers together, and all the variables

20x-4x*x+96=0

Wy multiply elements

-4x^2+20x+96=0

a = -4; b = 20; c = +96;
Δ = b2-4ac
Δ = 202-4·(-4)·96
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-44}{2*-4}=\frac{-64}{-8}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+44}{2*-4}=\frac{24}{-8}
=-3
$