1/2x+5=3.5x-7

Solution for 1/2x+5=3.5x-7 equation:

1/2x+5=3.5x-7

We move all terms to the left:

1/2x+5-(3.5x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3.5x+7+5=0

We multiply all the terms by the denominator


-(3.5x)*2x+7*2x+5*2x+1=0

We add all the numbers together, and all the variables

-(+3.5x)*2x+7*2x+5*2x+1=0

We multiply parentheses

-6x^2+7*2x+5*2x+1=0

Wy multiply elements

-6x^2+14x+10x+1=0

We add all the numbers together, and all the variables

-6x^2+24x+1=0

a = -6; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-6)·1
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*-6}=\frac{-24-10\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*-6}=\frac{-24+10\sqrt{6}}{-12}
$