10/2x+2=5x-32

Solution for 10/2x+2=5x-32 equation:

10/2x+2=5x-32

We move all terms to the left:

10/2x+2-(5x-32)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

10/2x-5x+32+2=0

We multiply all the terms by the denominator


-5x*2x+32*2x+2*2x+10=0

Wy multiply elements

-10x^2+64x+4x+10=0

We add all the numbers together, and all the variables

-10x^2+68x+10=0

a = -10; b = 68; c = +10;
Δ = b2-4ac
Δ = 682-4·(-10)·10
Δ = 5024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5024}=\sqrt{16*314}=\sqrt{16}*\sqrt{314}=4\sqrt{314}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{314}}{2*-10}=\frac{-68-4\sqrt{314}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{314}}{2*-10}=\frac{-68+4\sqrt{314}}{-20}
$