3x(x+5)-7x=47

Solution for 3x(x+5)-7x=47 equation:

3x(x+5)-7x=47

We move all terms to the left:

3x(x+5)-7x-(47)=0

We add all the numbers together, and all the variables

-7x+3x(x+5)-47=0

We multiply parentheses

3x^2-7x+15x-47=0

We add all the numbers together, and all the variables

3x^2+8x-47=0

a = 3; b = 8; c = -47;
Δ = b2-4ac
Δ = 82-4·3·(-47)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{157}}{2*3}=\frac{-8-2\sqrt{157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{157}}{2*3}=\frac{-8+2\sqrt{157}}{6}
$