1/2x+5(3+4x)=2x-8

Solution for 1/2x+5(3+4x)=2x-8 equation:

1/2x+5(3+4x)=2x-8

We move all terms to the left:

1/2x+5(3+4x)-(2x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+5(4x+3)-(2x-8)=0

We multiply parentheses

1/2x+20x-(2x-8)+15=0

We get rid of parentheses

1/2x+20x-2x+8+15=0

We multiply all the terms by the denominator


20x*2x-2x*2x+8*2x+15*2x+1=0

Wy multiply elements

40x^2-4x^2+16x+30x+1=0

We add all the numbers together, and all the variables

36x^2+46x+1=0

a = 36; b = 46; c = +1;
Δ = b2-4ac
Δ = 462-4·36·1
Δ = 1972
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:

$\sqrt{\Delta}=\sqrt{1972}=\sqrt{4*493}=\sqrt{4}*\sqrt{493}=2\sqrt{493}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{493}}{2*36}=\frac{-46-2\sqrt{493}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{493}}{2*36}=\frac{-46+2\sqrt{493}}{72}
$