0.5x+3.75=-1/2x-1.25

Solution for 0.5x+3.75=-1/2x-1.25 equation:

0.5x+3.75=-1/2x-1.25

We move all terms to the left:

0.5x+3.75-(-1/2x-1.25)=0


Domain of the equation: 2x-1.25)!=0

x∈R


We get rid of parentheses

0.5x+1/2x+1.25+3.75=0

We multiply all the terms by the denominator


(0.5x)*2x+(1.25)*2x+(3.75)*2x+1=0

We add all the numbers together, and all the variables

(+0.5x)*2x+(1.25)*2x+(3.75)*2x+1=0

We multiply parentheses

0x^2+2.5x+7.5x+1=0

We add all the numbers together, and all the variables

x^2+10x+1=0

a = 1; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·1·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{6}}{2*1}=\frac{-10-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{6}}{2*1}=\frac{-10+4\sqrt{6}}{2}
$