x(9x+2)=4x^2-31x+14

Solution for x(9x+2)=4x^2-31x+14 equation:

x(9x+2)=4x^2-31x+14

We move all terms to the left:

x(9x+2)-(4x^2-31x+14)=0

We multiply parentheses

9x^2+2x-(4x^2-31x+14)=0

We get rid of parentheses

9x^2-4x^2+2x+31x-14=0

We add all the numbers together, and all the variables

5x^2+33x-14=0

a = 5; b = 33; c = -14;
Δ = b2-4ac
Δ = 332-4·5·(-14)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-37}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+37}{2*5}=\frac{4}{10}
=2/5
$