0.375x-0.25=1/4x+1.25

Solution for 0.375x-0.25=1/4x+1.25 equation:

0.375x-0.25=1/4x+1.25

We move all terms to the left:

0.375x-0.25-(1/4x+1.25)=0


Domain of the equation: 4x+1.25)!=0

x∈R


We get rid of parentheses

0.375x-1/4x-1.25-0.25=0

We multiply all the terms by the denominator


(0.375x)*4x-(1.25)*4x-(0.25)*4x-1=0

We add all the numbers together, and all the variables

(+0.375x)*4x-(1.25)*4x-(0.25)*4x-1=0

We multiply parentheses

0x^2-5x-x-1=0

We add all the numbers together, and all the variables

x^2-6x-1=0

a = 1; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·1·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*1}=\frac{6-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*1}=\frac{6+2\sqrt{10}}{2}
$