/2x-5=3x+7

Solution for /2x-5=3x+7 equation:

/2x-5=3x+7

We move all terms to the left:

/2x-5-(3x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

/2x-3x-7-5=0

We multiply all the terms by the denominator


-3x*2x-7*2x-5*2x+=0

We add all the numbers together, and all the variables

-3x*2x-7*2x-5*2x=0

Wy multiply elements

-6x^2-14x-10x=0

We add all the numbers together, and all the variables

-6x^2-24x=0

a = -6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-6)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-6}=\frac{48}{-12}
=-4
$