1/4x+7=26x

Solution for 1/4x+7=26x equation:

1/4x+7=26x

We move all terms to the left:

1/4x+7-(26x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-26x+1/4x+7=0

We multiply all the terms by the denominator


-26x*4x+7*4x+1=0

Wy multiply elements

-104x^2+28x+1=0

a = -104; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-104)·1
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20\sqrt{3}}{2*-104}=\frac{-28-20\sqrt{3}}{-208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20\sqrt{3}}{2*-104}=\frac{-28+20\sqrt{3}}{-208}
$