(1/5)(x+10)+5x=25

Solution for (1/5)(x+10)+5x=25 equation:

(1/5)(x+10)+5x=25

We move all terms to the left:

(1/5)(x+10)+5x-(25)=0


Domain of the equation: 5)(x+10)!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)(x+10)+5x-25=0

We add all the numbers together, and all the variables

5x+(+1/5)(x+10)-25=0

We multiply parentheses ..

(+x^2+1/5*10)+5x-25=0

We multiply all the terms by the denominator


(+x^2+1+5x*5*10)-25*5*10)=0

We add all the numbers together, and all the variables

(+x^2+1+5x*5*10)=0

We get rid of parentheses

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

Wy multiply elements

x^2+250x*1+1=0

Wy multiply elements

x^2+250x+1=0

a = 1; b = 250; c = +1;
Δ = b2-4ac
Δ = 2502-4·1·1
Δ = 62496
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:

$\sqrt{\Delta}=\sqrt{62496}=\sqrt{144*434}=\sqrt{144}*\sqrt{434}=12\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-12\sqrt{434}}{2*1}=\frac{-250-12\sqrt{434}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+12\sqrt{434}}{2*1}=\frac{-250+12\sqrt{434}}{2}
$