-1+1/2x=-4x+149

Solution for -1+1/2x=-4x+149 equation:

-1+1/2x=-4x+149

We move all terms to the left:

-1+1/2x-(-4x+149)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+4x-149-1=0

We multiply all the terms by the denominator


4x*2x-149*2x-1*2x+1=0

Wy multiply elements

8x^2-298x-2x+1=0

We add all the numbers together, and all the variables

8x^2-300x+1=0

a = 8; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·8·1
Δ = 89968
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:

$\sqrt{\Delta}=\sqrt{89968}=\sqrt{16*5623}=\sqrt{16}*\sqrt{5623}=4\sqrt{5623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5623}}{2*8}=\frac{300-4\sqrt{5623}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5623}}{2*8}=\frac{300+4\sqrt{5623}}{16}
$