2x(2x+3x)-3x=14

Solution for 2x(2x+3x)-3x=14 equation:

2x(2x+3x)-3x=14

We move all terms to the left:

2x(2x+3x)-3x-(14)=0

We add all the numbers together, and all the variables

2x(+5x)-3x-14=0

We add all the numbers together, and all the variables

-3x+2x(+5x)-14=0

We multiply parentheses

10x^2-3x-14=0

a = 10; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·10·(-14)
Δ = 569
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{-(-3)-\sqrt{569}}{2*10}=\frac{3-\sqrt{569}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{569}}{2*10}=\frac{3+\sqrt{569}}{20}
$