2x(1/3x-5)=2

Solution for 2x(1/3x-5)=2 equation:

2x(1/3x-5)=2

We move all terms to the left:

2x(1/3x-5)-(2)=0


Domain of the equation: 3x-5)!=0

x∈R


We multiply parentheses

2x^2-10x-2=0

a = 2; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·2·(-2)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*2}=\frac{10-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*2}=\frac{10+2\sqrt{29}}{4}
$