32x-5=2(3x-2)x=1/26=0.038

Solution for 32x-5=2(3x-2)x=1/26=0.038 equation:

32x-5=2(3x-2)x=1/26=0.038

We move all terms to the left:

32x-5-(2(3x-2)x)=0


We calculate terms in parentheses: -(2(3x-2)x), so:

2(3x-2)x

We multiply parentheses

6x^2-4x

Back to the equation:

-(6x^2-4x)


We get rid of parentheses

-6x^2+32x+4x-5=0

We add all the numbers together, and all the variables

-6x^2+36x-5=0

a = -6; b = 36; c = -5;
Δ = b2-4ac
Δ = 362-4·(-6)·(-5)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-14\sqrt{6}}{2*-6}=\frac{-36-14\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+14\sqrt{6}}{2*-6}=\frac{-36+14\sqrt{6}}{-12}
$