10x-5=5/2x+10

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

10x-5=5/2x+10

We move all terms to the left:

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


Domain of the equation: 2x+10)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-20x-10x-5=0

We add all the numbers together, and all the variables

20x^2-30x-5=0

a = 20; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·20·(-5)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{13}}{2*20}=\frac{30-10\sqrt{13}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{13}}{2*20}=\frac{30+10\sqrt{13}}{40}
$