2(x-4)=3/5x+6

Solution for 2(x-4)=3/5x+6 equation:

2(x-4)=3/5x+6

We move all terms to the left:

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


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

x∈R


We multiply parentheses

2x-(3/5x+6)-8=0

We get rid of parentheses

2x-3/5x-6-8=0

We multiply all the terms by the denominator


2x*5x-6*5x-8*5x-3=0

Wy multiply elements

10x^2-30x-40x-3=0

We add all the numbers together, and all the variables

10x^2-70x-3=0

a = 10; b = -70; c = -3;
Δ = b2-4ac
Δ = -702-4·10·(-3)
Δ = 5020
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:

$\sqrt{\Delta}=\sqrt{5020}=\sqrt{4*1255}=\sqrt{4}*\sqrt{1255}=2\sqrt{1255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1255}}{2*10}=\frac{70-2\sqrt{1255}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1255}}{2*10}=\frac{70+2\sqrt{1255}}{20}
$