-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+26x-3=0

a = -10; b = 26; c = -3;
Δ = b2-4ac
Δ = 262-4·(-10)·(-3)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{139}}{2*-10}=\frac{-26-2\sqrt{139}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{139}}{2*-10}=\frac{-26+2\sqrt{139}}{-20}
$