0.5(x+20)=1/4x-5

Solution for 0.5(x+20)=1/4x-5 equation:

0.5(x+20)=1/4x-5

We move all terms to the left:

0.5(x+20)-(1/4x-5)=0


Domain of the equation: 4x-5)!=0

x∈R


We multiply parentheses

0.5x-(1/4x-5)+10=0

We get rid of parentheses

0.5x-1/4x+5+10=0

We multiply all the terms by the denominator


(0.5x)*4x+5*4x+10*4x-1=0

We add all the numbers together, and all the variables

(+0.5x)*4x+5*4x+10*4x-1=0

We multiply parentheses

0x^2+5*4x+10*4x-1=0

Wy multiply elements

0x^2+20x+40x-1=0

We add all the numbers together, and all the variables

x^2+60x-1=0

a = 1; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·1·(-1)
Δ = 3604
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:

$\sqrt{\Delta}=\sqrt{3604}=\sqrt{4*901}=\sqrt{4}*\sqrt{901}=2\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{901}}{2*1}=\frac{-60-2\sqrt{901}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{901}}{2*1}=\frac{-60+2\sqrt{901}}{2}
$