(1/5)(x-6)=4x-3(x-1)+(51/5)

Solution for (1/5)(x-6)=4x-3(x-1)+(51/5) equation:

(1/5)(x-6)=4x-3(x-1)+(51/5)

We move all terms to the left:

(1/5)(x-6)-(4x-3(x-1)+(51/5))=0


Domain of the equation: 5)(x-6)!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)(x-6)-(4x-3(x-1)+(+51/5))=0

We multiply parentheses ..

(+x^2+1/5*-6)-(4x-3(x-1)+(+51/5))=0

We calculate fractions


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

We multiply all the terms by the denominator


x^2+(-1x-3)=0

We get rid of parentheses

x^2-1x-3=0

a = 1; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·1·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{13}}{2*1}=\frac{1-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*1}=\frac{1+\sqrt{13}}{2}
$