(1/5)(3x+110)=5x

Solution for (1/5)(3x+110)=5x equation:

(1/5)(3x+110)=5x

We move all terms to the left:

(1/5)(3x+110)-(5x)=0


Domain of the equation: 5)(3x+110)!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)(3x+110)-5x=0

We add all the numbers together, and all the variables

-5x+(+1/5)(3x+110)=0

We multiply parentheses ..

(+3x^2+1/5*110)-5x=0

We multiply all the terms by the denominator


(+3x^2+1-5x*5*110)=0

We get rid of parentheses

3x^2-5x*5*110+1=0

Wy multiply elements

3x^2-2750x*1+1=0

Wy multiply elements

3x^2-2750x+1=0

a = 3; b = -2750; c = +1;
Δ = b2-4ac
Δ = -27502-4·3·1
Δ = 7562488
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:

$\sqrt{\Delta}=\sqrt{7562488}=\sqrt{4*1890622}=\sqrt{4}*\sqrt{1890622}=2\sqrt{1890622}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2750)-2\sqrt{1890622}}{2*3}=\frac{2750-2\sqrt{1890622}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2750)+2\sqrt{1890622}}{2*3}=\frac{2750+2\sqrt{1890622}}{6}
$