2x+3x(5x-7)=47

Solution for 2x+3x(5x-7)=47 equation:

2x+3x(5x-7)=47

We move all terms to the left:

2x+3x(5x-7)-(47)=0

We multiply parentheses

15x^2+2x-21x-47=0

We add all the numbers together, and all the variables

15x^2-19x-47=0

a = 15; b = -19; c = -47;
Δ = b2-4ac
Δ = -192-4·15·(-47)
Δ = 3181
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{-(-19)-\sqrt{3181}}{2*15}=\frac{19-\sqrt{3181}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{3181}}{2*15}=\frac{19+\sqrt{3181}}{30}
$