(3x+8)(x-1)=47

Solution for (3x+8)(x-1)=47 equation:

(3x+8)(x-1)=47

We move all terms to the left:

(3x+8)(x-1)-(47)=0

We multiply parentheses ..

(+3x^2-3x+8x-8)-47=0

We get rid of parentheses

3x^2-3x+8x-8-47=0

We add all the numbers together, and all the variables

3x^2+5x-55=0

a = 3; b = 5; c = -55;
Δ = b2-4ac
Δ = 52-4·3·(-55)
Δ = 685
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{-(5)-\sqrt{685}}{2*3}=\frac{-5-\sqrt{685}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{685}}{2*3}=\frac{-5+\sqrt{685}}{6}
$