1/2x+125=4x-120

Solution for 1/2x+125=4x-120 equation:

1/2x+125=4x-120

We move all terms to the left:

1/2x+125-(4x-120)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x+120+125=0

We multiply all the terms by the denominator


-4x*2x+120*2x+125*2x+1=0

Wy multiply elements

-8x^2+240x+250x+1=0

We add all the numbers together, and all the variables

-8x^2+490x+1=0

a = -8; b = 490; c = +1;
Δ = b2-4ac
Δ = 4902-4·(-8)·1
Δ = 240132
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:

$\sqrt{\Delta}=\sqrt{240132}=\sqrt{4*60033}=\sqrt{4}*\sqrt{60033}=2\sqrt{60033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(490)-2\sqrt{60033}}{2*-8}=\frac{-490-2\sqrt{60033}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(490)+2\sqrt{60033}}{2*-8}=\frac{-490+2\sqrt{60033}}{-16}
$