(5x+4)(x-1)=14

Solution for (5x+4)(x-1)=14 equation:

(5x+4)(x-1)=14

We move all terms to the left:

(5x+4)(x-1)-(14)=0

We multiply parentheses ..

(+5x^2-5x+4x-4)-14=0

We get rid of parentheses

5x^2-5x+4x-4-14=0

We add all the numbers together, and all the variables

5x^2-1x-18=0

a = 5; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·5·(-18)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*5}=\frac{-18}{10}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*5}=\frac{20}{10}
=2
$