(5x+1)*(x-3)=120

Solution for (5x+1)*(x-3)=120 equation:

(5x+1)(x-3)=120

We move all terms to the left:

(5x+1)(x-3)-(120)=0

We multiply parentheses ..

(+5x^2-15x+x-3)-120=0

We get rid of parentheses

5x^2-15x+x-3-120=0

We add all the numbers together, and all the variables

5x^2-14x-123=0

a = 5; b = -14; c = -123;
Δ = b2-4ac
Δ = -142-4·5·(-123)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{166}}{2*5}=\frac{14-4\sqrt{166}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{166}}{2*5}=\frac{14+4\sqrt{166}}{10}
$