(5x-3)(x-1)=39

Solution for (5x-3)(x-1)=39 equation:

(5x-3)(x-1)=39

We move all terms to the left:

(5x-3)(x-1)-(39)=0

We multiply parentheses ..

(+5x^2-5x-3x+3)-39=0

We get rid of parentheses

5x^2-5x-3x+3-39=0

We add all the numbers together, and all the variables

5x^2-8x-36=0

a = 5; b = -8; c = -36;
Δ = b2-4ac
Δ = -82-4·5·(-36)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*5}=\frac{36}{10}
=3+3/5
$