(1/10)(x+50)=-3x-13+4x

Solution for (1/10)(x+50)=-3x-13+4x equation:

(1/10)(x+50)=-3x-13+4x

We move all terms to the left:

(1/10)(x+50)-(-3x-13+4x)=0


Domain of the equation: 10)(x+50)!=0

x∈R


We add all the numbers together, and all the variables

(+1/10)(x+50)-(x-13)=0

We get rid of parentheses

(+1/10)(x+50)-x+13=0

We multiply parentheses ..

(+x^2+1/10*50)-x+13=0

We multiply all the terms by the denominator


(+x^2+1-x*10*50)+13*10*50)=0

We add all the numbers together, and all the variables

(+x^2+1-x*10*50)=0

We get rid of parentheses

x^2-x*10*50+1=0

Wy multiply elements

x^2-500x*5+1=0

Wy multiply elements

x^2-2500x+1=0

a = 1; b = -2500; c = +1;
Δ = b2-4ac
Δ = -25002-4·1·1
Δ = 6249996
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:

$\sqrt{\Delta}=\sqrt{6249996}=\sqrt{36*173611}=\sqrt{36}*\sqrt{173611}=6\sqrt{173611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-6\sqrt{173611}}{2*1}=\frac{2500-6\sqrt{173611}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+6\sqrt{173611}}{2*1}=\frac{2500+6\sqrt{173611}}{2}
$