(3x+10)(9x-39)=47

Solution for (3x+10)(9x-39)=47 equation:

(3x+10)(9x-39)=47

We move all terms to the left:

(3x+10)(9x-39)-(47)=0

We multiply parentheses ..

(+27x^2-117x+90x-390)-47=0

We get rid of parentheses

27x^2-117x+90x-390-47=0

We add all the numbers together, and all the variables

27x^2-27x-437=0

a = 27; b = -27; c = -437;
Δ = b2-4ac
Δ = -272-4·27·(-437)
Δ = 47925
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{47925}=\sqrt{225*213}=\sqrt{225}*\sqrt{213}=15\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-15\sqrt{213}}{2*27}=\frac{27-15\sqrt{213}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+15\sqrt{213}}{2*27}=\frac{27+15\sqrt{213}}{54}
$