2x-3=1/4x+4

Solution for 2x-3=1/4x+4 equation:

2x-3=1/4x+4

We move all terms to the left:

2x-3-(1/4x+4)=0


Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

2x-1/4x-4-3=0

We multiply all the terms by the denominator


2x*4x-4*4x-3*4x-1=0

Wy multiply elements

8x^2-16x-12x-1=0

We add all the numbers together, and all the variables

8x^2-28x-1=0

a = 8; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·8·(-1)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{51}}{2*8}=\frac{28-4\sqrt{51}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{51}}{2*8}=\frac{28+4\sqrt{51}}{16}
$