1/5x-6=-3x+10

Solution for 1/5x-6=-3x+10 equation:

1/5x-6=-3x+10

We move all terms to the left:

1/5x-6-(-3x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x+3x-10-6=0

We multiply all the terms by the denominator


3x*5x-10*5x-6*5x+1=0

Wy multiply elements

15x^2-50x-30x+1=0

We add all the numbers together, and all the variables

15x^2-80x+1=0

a = 15; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·15·1
Δ = 6340
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:

$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1585}}{2*15}=\frac{80-2\sqrt{1585}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1585}}{2*15}=\frac{80+2\sqrt{1585}}{30}
$