(5x+1)(4x-2)=2x+14

Solution for (5x+1)(4x-2)=2x+14 equation:

(5x+1)(4x-2)=2x+14

We move all terms to the left:

(5x+1)(4x-2)-(2x+14)=0

We get rid of parentheses

(5x+1)(4x-2)-2x-14=0

We multiply parentheses ..

(+20x^2-10x+4x-2)-2x-14=0

We get rid of parentheses

20x^2-10x+4x-2x-2-14=0

We add all the numbers together, and all the variables

20x^2-8x-16=0

a = 20; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·20·(-16)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{21}}{2*20}=\frac{8-8\sqrt{21}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{21}}{2*20}=\frac{8+8\sqrt{21}}{40}
$