-1/4*x+120=1/2*x+30

Solution for -1/4*x+120=1/2*x+30 equation:

-1/4*x+120=1/2x+30

We move all terms to the left:

-1/4*x+120-(1/2x+30)=0


Domain of the equation: 4*x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

-1/4*x-1/2x-30+120=0

We calculate fractions


(-4x^2)/16x^2+(-2x)/16x^2-30+120=0

We add all the numbers together, and all the variables

(-4x^2)/16x^2+(-2x)/16x^2+90=0

We multiply all the terms by the denominator


(-4x^2)+(-2x)+90*16x^2=0

Wy multiply elements

(-4x^2)+1440x^2+(-2x)=0

We get rid of parentheses

-4x^2+1440x^2-2x=0

We add all the numbers together, and all the variables

1436x^2-2x=0

a = 1436; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·1436·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*1436}=\frac{0}{2872}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*1436}=\frac{4}{2872}
=1/718
$