1/2x+25=3x

Solution for 1/2x+25=3x equation:

1/2x+25=3x

We move all terms to the left:

1/2x+25-(3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/2x+25=0

We multiply all the terms by the denominator


-3x*2x+25*2x+1=0

Wy multiply elements

-6x^2+50x+1=0

a = -6; b = 50; c = +1;
Δ = b2-4ac
Δ = 502-4·(-6)·1
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{631}}{2*-6}=\frac{-50-2\sqrt{631}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{631}}{2*-6}=\frac{-50+2\sqrt{631}}{-12}
$