5x-7=3/2x-6

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

5x-7=3/2x-6

We move all terms to the left:

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


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2+12x-14x-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}
$