10x-53=(-13/2x)+46

Solution for 10x-53=(-13/2x)+46 equation:

10x-53=(-13/2x)+46

We move all terms to the left:

10x-53-((-13/2x)+46)=0


Domain of the equation: 2x)+46)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x)+46)-((-53*2x)+46)-13=0

Wy multiply elements

20x^2-106x=0

a = 20; b = -106; c = 0;
Δ = b2-4ac
Δ = -1062-4·20·0
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-106}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+106}{2*20}=\frac{212}{40}
=5+3/10
$