2.5x+7/2x-3=5x+7

Solution for 2.5x+7/2x-3=5x+7 equation:

2.5x+7/2x-3=5x+7

We move all terms to the left:

2.5x+7/2x-3-(5x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

2.5x+7/2x-5x-7-3=0

We multiply all the terms by the denominator


(2.5x)*2x-5x*2x-7*2x-3*2x+7=0

We add all the numbers together, and all the variables

(+2.5x)*2x-5x*2x-7*2x-3*2x+7=0

We multiply parentheses

4x^2-5x*2x-7*2x-3*2x+7=0

Wy multiply elements

4x^2-10x^2-14x-6x+7=0

We add all the numbers together, and all the variables

-6x^2-20x+7=0

a = -6; b = -20; c = +7;
Δ = b2-4ac
Δ = -202-4·(-6)·7
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{142}}{2*-6}=\frac{20-2\sqrt{142}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{142}}{2*-6}=\frac{20+2\sqrt{142}}{-12}
$