5-2(3x-4)x=1

Solution for 5-2(3x-4)x=1 equation:

5-2(3x-4)x=1

We move all terms to the left:

5-2(3x-4)x-(1)=0

We add all the numbers together, and all the variables

-2(3x-4)x+4=0

We multiply parentheses

-6x^2+8x+4=0

a = -6; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-6)·4
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*-6}=\frac{-8-4\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*-6}=\frac{-8+4\sqrt{10}}{-12}
$