x(5x+1)=2x^2-18x+14

Solution for x(5x+1)=2x^2-18x+14 equation:

x(5x+1)=2x^2-18x+14

We move all terms to the left:

x(5x+1)-(2x^2-18x+14)=0

We multiply parentheses

5x^2+x-(2x^2-18x+14)=0

We get rid of parentheses

5x^2-2x^2+x+18x-14=0

We add all the numbers together, and all the variables

3x^2+19x-14=0

a = 3; b = 19; c = -14;
Δ = b2-4ac
Δ = 192-4·3·(-14)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*3}=\frac{4}{6}
=2/3
$