5x+13=3(x+4)2x+1

Solution for 5x+13=3(x+4)2x+1 equation:

5x+13=3(x+4)2x+1

We move all terms to the left:

5x+13-(3(x+4)2x+1)=0


We calculate terms in parentheses: -(3(x+4)2x+1), so:

3(x+4)2x+1

We multiply parentheses

6x^2+24x+1

Back to the equation:

-(6x^2+24x+1)


We get rid of parentheses

-6x^2+5x-24x-1+13=0

We add all the numbers together, and all the variables

-6x^2-19x+12=0

a = -6; b = -19; c = +12;
Δ = b2-4ac
Δ = -192-4·(-6)·12
Δ = 649
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{-(-19)-\sqrt{649}}{2*-6}=\frac{19-\sqrt{649}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{649}}{2*-6}=\frac{19+\sqrt{649}}{-12}
$