5x(3x+8)+2=5

Solution for 5x(3x+8)+2=5 equation:

5x(3x+8)+2=5

We move all terms to the left:

5x(3x+8)+2-(5)=0

We add all the numbers together, and all the variables

5x(3x+8)-3=0

We multiply parentheses

15x^2+40x-3=0

a = 15; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·15·(-3)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{445}}{2*15}=\frac{-40-2\sqrt{445}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{445}}{2*15}=\frac{-40+2\sqrt{445}}{30}
$