1/26x-10=-4x+30

Solution for 1/26x-10=-4x+30 equation:

1/26x-10=-4x+30

We move all terms to the left:

1/26x-10-(-4x+30)=0


Domain of the equation: 26x!=0

x!=0/26

x!=0

x∈R


We get rid of parentheses

1/26x+4x-30-10=0

We multiply all the terms by the denominator


4x*26x-30*26x-10*26x+1=0

Wy multiply elements

104x^2-780x-260x+1=0

We add all the numbers together, and all the variables

104x^2-1040x+1=0

a = 104; b = -1040; c = +1;
Δ = b2-4ac
Δ = -10402-4·104·1
Δ = 1081184
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:

$\sqrt{\Delta}=\sqrt{1081184}=\sqrt{16*67574}=\sqrt{16}*\sqrt{67574}=4\sqrt{67574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1040)-4\sqrt{67574}}{2*104}=\frac{1040-4\sqrt{67574}}{208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1040)+4\sqrt{67574}}{2*104}=\frac{1040+4\sqrt{67574}}{208}
$