2/4x+5=7x-8

Solution for 2/4x+5=7x-8 equation:

2/4x+5=7x-8

We move all terms to the left:

2/4x+5-(7x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-7x+8+5=0

We multiply all the terms by the denominator


-7x*4x+8*4x+5*4x+2=0

Wy multiply elements

-28x^2+32x+20x+2=0

We add all the numbers together, and all the variables

-28x^2+52x+2=0

a = -28; b = 52; c = +2;
Δ = b2-4ac
Δ = 522-4·(-28)·2
Δ = 2928
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:

$\sqrt{\Delta}=\sqrt{2928}=\sqrt{16*183}=\sqrt{16}*\sqrt{183}=4\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{183}}{2*-28}=\frac{-52-4\sqrt{183}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{183}}{2*-28}=\frac{-52+4\sqrt{183}}{-56}
$