7/2x-6=2x+5

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

7/2x-6=2x+5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-10x-12x+7=0

We add all the numbers together, and all the variables

-4x^2-22x+7=0

a = -4; b = -22; c = +7;
Δ = b2-4ac
Δ = -222-4·(-4)·7
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{149}}{2*-4}=\frac{22-2\sqrt{149}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{149}}{2*-4}=\frac{22+2\sqrt{149}}{-8}
$