2x-4+1/2x+7=3x-5x+27-10

Solution for 2x-4+1/2x+7=3x-5x+27-10 equation:

2x-4+1/2x+7=3x-5x+27-10

We move all terms to the left:

2x-4+1/2x+7-(3x-5x+27-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-(-2x+17)-4+7=0

We add all the numbers together, and all the variables

2x+1/2x-(-2x+17)+3=0

We get rid of parentheses

2x+1/2x+2x-17+3=0

We multiply all the terms by the denominator


2x*2x+2x*2x-17*2x+3*2x+1=0

Wy multiply elements

4x^2+4x^2-34x+6x+1=0

We add all the numbers together, and all the variables

8x^2-28x+1=0

a = 8; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·8·1
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{47}}{2*8}=\frac{28-4\sqrt{47}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{47}}{2*8}=\frac{28+4\sqrt{47}}{16}
$