5x(9x+24)=x

Solution for 5x(9x+24)=x equation:

5x(9x+24)=x

We move all terms to the left:

5x(9x+24)-(x)=0

We add all the numbers together, and all the variables

-1x+5x(9x+24)=0

We multiply parentheses

45x^2-1x+120x=0

We add all the numbers together, and all the variables

45x^2+119x=0

a = 45; b = 119; c = 0;
Δ = b2-4ac
Δ = 1192-4·45·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-119}{2*45}=\frac{-238}{90}
=-2+29/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+119}{2*45}=\frac{0}{90}
=0
$