1/4x-5=-2x+13

Solution for 1/4x-5=-2x+13 equation:

1/4x-5=-2x+13

We move all terms to the left:

1/4x-5-(-2x+13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+2x-13-5=0

We multiply all the terms by the denominator


2x*4x-13*4x-5*4x+1=0

Wy multiply elements

8x^2-52x-20x+1=0

We add all the numbers together, and all the variables

8x^2-72x+1=0

a = 8; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·8·1
Δ = 5152
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:

$\sqrt{\Delta}=\sqrt{5152}=\sqrt{16*322}=\sqrt{16}*\sqrt{322}=4\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{322}}{2*8}=\frac{72-4\sqrt{322}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{322}}{2*8}=\frac{72+4\sqrt{322}}{16}
$