-6x=1/2x-25

Solution for -6x=1/2x-25 equation:

-6x=1/2x-25

We move all terms to the left:

-6x-(1/2x-25)=0


Domain of the equation: 2x-25)!=0

x∈R


We get rid of parentheses

-6x-1/2x+25=0

We multiply all the terms by the denominator


-6x*2x+25*2x-1=0

Wy multiply elements

-12x^2+50x-1=0

a = -12; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·(-12)·(-1)
Δ = 2452
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:

$\sqrt{\Delta}=\sqrt{2452}=\sqrt{4*613}=\sqrt{4}*\sqrt{613}=2\sqrt{613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{613}}{2*-12}=\frac{-50-2\sqrt{613}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{613}}{2*-12}=\frac{-50+2\sqrt{613}}{-24}
$