1/4x+3=7x-6

Solution for 1/4x+3=7x-6 equation:

1/4x+3=7x-6

We move all terms to the left:

1/4x+3-(7x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-7x+6+3=0

We multiply all the terms by the denominator


-7x*4x+6*4x+3*4x+1=0

Wy multiply elements

-28x^2+24x+12x+1=0

We add all the numbers together, and all the variables

-28x^2+36x+1=0

a = -28; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-28)·1
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{22}}{2*-28}=\frac{-36-8\sqrt{22}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{22}}{2*-28}=\frac{-36+8\sqrt{22}}{-56}
$