(2x-1)(3x+8)=6(x+4)

Solution for (2x-1)(3x+8)=6(x+4) equation:

(2x-1)(3x+8)=6(x+4)

We move all terms to the left:

(2x-1)(3x+8)-(6(x+4))=0

We multiply parentheses ..

(+6x^2+16x-3x-8)-(6(x+4))=0


We calculate terms in parentheses: -(6(x+4)), so:

6(x+4)

We multiply parentheses

6x+24

Back to the equation:

-(6x+24)


We get rid of parentheses

6x^2+16x-3x-6x-8-24=0

We add all the numbers together, and all the variables

6x^2+7x-32=0

a = 6; b = 7; c = -32;
Δ = b2-4ac
Δ = 72-4·6·(-32)
Δ = 817
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{-(7)-\sqrt{817}}{2*6}=\frac{-7-\sqrt{817}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{817}}{2*6}=\frac{-7+\sqrt{817}}{12}
$