3/2x-6=5x-7

Solution for 3/2x-6=5x-7 equation:

3/2x-6=5x-7

We move all terms to the left:

3/2x-6-(5x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-5x+7-6=0

We multiply all the terms by the denominator


-5x*2x+7*2x-6*2x+3=0

Wy multiply elements

-10x^2+14x-12x+3=0

We add all the numbers together, and all the variables

-10x^2+2x+3=0

a = -10; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-10)·3
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*-10}=\frac{-2-2\sqrt{31}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*-10}=\frac{-2+2\sqrt{31}}{-20}
$