1-2x=-5/4x+2

Solution for 1-2x=-5/4x+2 equation:

1-2x=-5/4x+2

We move all terms to the left:

1-2x-(-5/4x+2)=0


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

-2x+5/4x-2+1=0

We multiply all the terms by the denominator


-2x*4x-2*4x+1*4x+5=0

Wy multiply elements

-8x^2-8x+4x+5=0

We add all the numbers together, and all the variables

-8x^2-4x+5=0

a = -8; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-8)·5
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*-8}=\frac{4-4\sqrt{11}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*-8}=\frac{4+4\sqrt{11}}{-16}
$