5x(x+4)=3x+8

Solution for 5x(x+4)=3x+8 equation:

5x(x+4)=3x+8

We move all terms to the left:

5x(x+4)-(3x+8)=0

We multiply parentheses

5x^2+20x-(3x+8)=0

We get rid of parentheses

5x^2+20x-3x-8=0

We add all the numbers together, and all the variables

5x^2+17x-8=0

a = 5; b = 17; c = -8;
Δ = b2-4ac
Δ = 172-4·5·(-8)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{449}}{2*5}=\frac{-17-\sqrt{449}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{449}}{2*5}=\frac{-17+\sqrt{449}}{10}
$