3x-4=-1/2x+10

Solution for 3x-4=-1/2x+10 equation:

3x-4=-1/2x+10

We move all terms to the left:

3x-4-(-1/2x+10)=0


Domain of the equation: 2x+10)!=0

x∈R


We get rid of parentheses

3x+1/2x-10-4=0

We multiply all the terms by the denominator


3x*2x-10*2x-4*2x+1=0

Wy multiply elements

6x^2-20x-8x+1=0

We add all the numbers together, and all the variables

6x^2-28x+1=0

a = 6; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·6·1
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{190}}{2*6}=\frac{28-2\sqrt{190}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{190}}{2*6}=\frac{28+2\sqrt{190}}{12}
$