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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+5x^2-5x+3x-3)-1=0

We get rid of parentheses

5x^2-5x+3x-3-1=0

We add all the numbers together, and all the variables

5x^2-2x-4=0

a = 5; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·5·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*5}=\frac{2-2\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*5}=\frac{2+2\sqrt{21}}{10}
$