3x2+13x=8(x+1)

Solution for 3x2+13x=8(x+1) equation:

3x^2+13x=8(x+1)

We move all terms to the left:

3x^2+13x-(8(x+1))=0


We calculate terms in parentheses: -(8(x+1)), so:

8(x+1)

We multiply parentheses

8x+8

Back to the equation:

-(8x+8)


We get rid of parentheses

3x^2+13x-8x-8=0

We add all the numbers together, and all the variables

3x^2+5x-8=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$