7/2x-1=2x+8

Solution for 7/2x-1=2x+8 equation:

7/2x-1=2x+8

We move all terms to the left:

7/2x-1-(2x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-2x-8-1=0

We multiply all the terms by the denominator


-2x*2x-8*2x-1*2x+7=0

Wy multiply elements

-4x^2-16x-2x+7=0

We add all the numbers together, and all the variables

-4x^2-18x+7=0

a = -4; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·(-4)·7
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{109}}{2*-4}=\frac{18-2\sqrt{109}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{109}}{2*-4}=\frac{18+2\sqrt{109}}{-8}
$