5+5x=-4+1/2x

Solution for 5+5x=-4+1/2x equation:

5+5x=-4+1/2x

We move all terms to the left:

5+5x-(-4+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(1/2x-4)+5=0

We get rid of parentheses

5x-1/2x+4+5=0

We multiply all the terms by the denominator


5x*2x+4*2x+5*2x-1=0

Wy multiply elements

10x^2+8x+10x-1=0

We add all the numbers together, and all the variables

10x^2+18x-1=0

a = 10; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·10·(-1)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{91}}{2*10}=\frac{-18-2\sqrt{91}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{91}}{2*10}=\frac{-18+2\sqrt{91}}{20}
$