10(x+2)=-10-5/4x

Solution for 10(x+2)=-10-5/4x equation:

10(x+2)=-10-5/4x

We move all terms to the left:

10(x+2)-(-10-5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10(x+2)-(-5/4x-10)=0

We multiply parentheses

10x-(-5/4x-10)+20=0

We get rid of parentheses

10x+5/4x+10+20=0

We multiply all the terms by the denominator


10x*4x+10*4x+20*4x+5=0

Wy multiply elements

40x^2+40x+80x+5=0

We add all the numbers together, and all the variables

40x^2+120x+5=0

a = 40; b = 120; c = +5;
Δ = b2-4ac
Δ = 1202-4·40·5
Δ = 13600
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:

$\sqrt{\Delta}=\sqrt{13600}=\sqrt{400*34}=\sqrt{400}*\sqrt{34}=20\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{34}}{2*40}=\frac{-120-20\sqrt{34}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{34}}{2*40}=\frac{-120+20\sqrt{34}}{80}
$