4x(x+5)=3x+2

Solution for 4x(x+5)=3x+2 equation:

4x(x+5)=3x+2

We move all terms to the left:

4x(x+5)-(3x+2)=0

We multiply parentheses

4x^2+20x-(3x+2)=0

We get rid of parentheses

4x^2+20x-3x-2=0

We add all the numbers together, and all the variables

4x^2+17x-2=0

a = 4; b = 17; c = -2;
Δ = b2-4ac
Δ = 172-4·4·(-2)
Δ = 321
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{321}}{2*4}=\frac{-17-\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{321}}{2*4}=\frac{-17+\sqrt{321}}{8}
$