-x+1=1/4x-1.5

Solution for -x+1=1/4x-1.5 equation:

-x+1=1/4x-1.5

We move all terms to the left:

-x+1-(1/4x-1.5)=0


Domain of the equation: 4x-1.5)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/4x-1.5)+1=0

We get rid of parentheses

-1x-1/4x+1.5+1=0

We multiply all the terms by the denominator


-1x*4x+(1.5)*4x+1*4x-1=0

We multiply parentheses

-1x*4x+6x+1*4x-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2+10x-1=0

a = -4; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-4)·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*-4}=\frac{-10-2\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*-4}=\frac{-10+2\sqrt{21}}{-8}
$