1/2x-10=5x-55

Solution for 1/2x-10=5x-55 equation:

1/2x-10=5x-55

We move all terms to the left:

1/2x-10-(5x-55)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-5x+55-10=0

We multiply all the terms by the denominator


-5x*2x+55*2x-10*2x+1=0

Wy multiply elements

-10x^2+110x-20x+1=0

We add all the numbers together, and all the variables

-10x^2+90x+1=0

a = -10; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-10)·1
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2035}}{2*-10}=\frac{-90-2\sqrt{2035}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2035}}{2*-10}=\frac{-90+2\sqrt{2035}}{-20}
$