24-1/2x=7x-6

Solution for 24-1/2x=7x-6 equation:

24-1/2x=7x-6

We move all terms to the left:

24-1/2x-(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+24=0

We multiply all the terms by the denominator


-7x*2x+6*2x+24*2x-1=0

Wy multiply elements

-14x^2+12x+48x-1=0

We add all the numbers together, and all the variables

-14x^2+60x-1=0

a = -14; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·(-14)·(-1)
Δ = 3544
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:

$\sqrt{\Delta}=\sqrt{3544}=\sqrt{4*886}=\sqrt{4}*\sqrt{886}=2\sqrt{886}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{886}}{2*-14}=\frac{-60-2\sqrt{886}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{886}}{2*-14}=\frac{-60+2\sqrt{886}}{-28}
$