X-1/4x-19=7

Solution for X-1/4x-19=7 equation:

X-1/4X-19=7

We move all terms to the left:

X-1/4X-19-(7)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

X-1/4X-26=0

We multiply all the terms by the denominator


X*4X-26*4X-1=0

Wy multiply elements

4X^2-104X-1=0

a = 4; b = -104; c = -1;
Δ = b2-4ac
Δ = -1042-4·4·(-1)
Δ = 10832
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:

$\sqrt{\Delta}=\sqrt{10832}=\sqrt{16*677}=\sqrt{16}*\sqrt{677}=4\sqrt{677}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{677}}{2*4}=\frac{104-4\sqrt{677}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{677}}{2*4}=\frac{104+4\sqrt{677}}{8}
$