-1/4x-3=x+7

Solution for -1/4x-3=x+7 equation:

-1/4x-3=x+7

We move all terms to the left:

-1/4x-3-(x+7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x-x-7-3=0

We multiply all the terms by the denominator


-x*4x-7*4x-3*4x-1=0

Wy multiply elements

-4x^2-28x-12x-1=0

We add all the numbers together, and all the variables

-4x^2-40x-1=0

a = -4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·(-4)·(-1)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*-4}=\frac{40-12\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*-4}=\frac{40+12\sqrt{11}}{-8}
$