2(x+7)=3/48x+4

Solution for 2(x+7)=3/48x+4 equation:

2(x+7)=3/48x+4

We move all terms to the left:

2(x+7)-(3/48x+4)=0


Domain of the equation: 48x+4)!=0

x∈R


We multiply parentheses

2x-(3/48x+4)+14=0

We get rid of parentheses

2x-3/48x-4+14=0

We multiply all the terms by the denominator


2x*48x-4*48x+14*48x-3=0

Wy multiply elements

96x^2-192x+672x-3=0

We add all the numbers together, and all the variables

96x^2+480x-3=0

a = 96; b = 480; c = -3;
Δ = b2-4ac
Δ = 4802-4·96·(-3)
Δ = 231552
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:

$\sqrt{\Delta}=\sqrt{231552}=\sqrt{576*402}=\sqrt{576}*\sqrt{402}=24\sqrt{402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-24\sqrt{402}}{2*96}=\frac{-480-24\sqrt{402}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+24\sqrt{402}}{2*96}=\frac{-480+24\sqrt{402}}{192}
$