1/2x+10-3x=34

Solution for 1/2x+10-3x=34 equation:

1/2x+10-3x=34

We move all terms to the left:

1/2x+10-3x-(34)=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-24=0

We multiply all the terms by the denominator


-3x*2x-24*2x+1=0

Wy multiply elements

-6x^2-48x+1=0

a = -6; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·(-6)·1
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{582}}{2*-6}=\frac{48-2\sqrt{582}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{582}}{2*-6}=\frac{48+2\sqrt{582}}{-12}
$