(2x+3)=(x+8)(3x+1)

Solution for (2x+3)=(x+8)(3x+1) equation:

(2x+3)=(x+8)(3x+1)

We move all terms to the left:

(2x+3)-((x+8)(3x+1))=0

We get rid of parentheses

2x-((x+8)(3x+1))+3=0

We multiply parentheses ..

-((+3x^2+x+24x+8))+2x+3=0


We calculate terms in parentheses: -((+3x^2+x+24x+8)), so:

(+3x^2+x+24x+8)

We get rid of parentheses

3x^2+x+24x+8

We add all the numbers together, and all the variables

3x^2+25x+8

Back to the equation:

-(3x^2+25x+8)


We add all the numbers together, and all the variables

2x-(3x^2+25x+8)+3=0

We get rid of parentheses

-3x^2+2x-25x-8+3=0

We add all the numbers together, and all the variables

-3x^2-23x-5=0

a = -3; b = -23; c = -5;
Δ = b2-4ac
Δ = -232-4·(-3)·(-5)
Δ = 469
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{-(-23)-\sqrt{469}}{2*-3}=\frac{23-\sqrt{469}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{469}}{2*-3}=\frac{23+\sqrt{469}}{-6}
$