-1/2x+30=-2x+3

Solution for -1/2x+30=-2x+3 equation:

-1/2x+30=-2x+3

We move all terms to the left:

-1/2x+30-(-2x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x+2x-3+30=0

We multiply all the terms by the denominator


2x*2x-3*2x+30*2x-1=0

Wy multiply elements

4x^2-6x+60x-1=0

We add all the numbers together, and all the variables

4x^2+54x-1=0

a = 4; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·4·(-1)
Δ = 2932
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:

$\sqrt{\Delta}=\sqrt{2932}=\sqrt{4*733}=\sqrt{4}*\sqrt{733}=2\sqrt{733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{733}}{2*4}=\frac{-54-2\sqrt{733}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{733}}{2*4}=\frac{-54+2\sqrt{733}}{8}
$