15-1/2x=7x-6

Solution for 15-1/2x=7x-6 equation:

15-1/2x=7x-6

We move all terms to the left:

15-1/2x-(7x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-7x+6+15=0

We multiply all the terms by the denominator


-7x*2x+6*2x+15*2x-1=0

Wy multiply elements

-14x^2+12x+30x-1=0

We add all the numbers together, and all the variables

-14x^2+42x-1=0

a = -14; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·(-14)·(-1)
Δ = 1708
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:

$\sqrt{\Delta}=\sqrt{1708}=\sqrt{4*427}=\sqrt{4}*\sqrt{427}=2\sqrt{427}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{427}}{2*-14}=\frac{-42-2\sqrt{427}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{427}}{2*-14}=\frac{-42+2\sqrt{427}}{-28}
$