5x(-6x-8)=2x+14

Solution for 5x(-6x-8)=2x+14 equation:

5x(-6x-8)=2x+14

We move all terms to the left:

5x(-6x-8)-(2x+14)=0

We multiply parentheses

-30x^2-40x-(2x+14)=0

We get rid of parentheses

-30x^2-40x-2x-14=0

We add all the numbers together, and all the variables

-30x^2-42x-14=0

a = -30; b = -42; c = -14;
Δ = b2-4ac
Δ = -422-4·(-30)·(-14)
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{-(-42)-2\sqrt{21}}{2*-30}=\frac{42-2\sqrt{21}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{21}}{2*-30}=\frac{42+2\sqrt{21}}{-60}
$