5/2x+6=7x-8

Solution for 5/2x+6=7x-8 equation:

5/2x+6=7x-8

We move all terms to the left:

5/2x+6-(7x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-7x+8+6=0

We multiply all the terms by the denominator


-7x*2x+8*2x+6*2x+5=0

Wy multiply elements

-14x^2+16x+12x+5=0

We add all the numbers together, and all the variables

-14x^2+28x+5=0

a = -14; b = 28; c = +5;
Δ = b2-4ac
Δ = 282-4·(-14)·5
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{266}}{2*-14}=\frac{-28-2\sqrt{266}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{266}}{2*-14}=\frac{-28+2\sqrt{266}}{-28}
$