5x-14=x(24+4x)

Solution for 5x-14=x(24+4x) equation:

5x-14=x(24+4x)

We move all terms to the left:

5x-14-(x(24+4x))=0

We add all the numbers together, and all the variables

5x-(x(4x+24))-14=0


We calculate terms in parentheses: -(x(4x+24)), so:

x(4x+24)

We multiply parentheses

4x^2+24x

Back to the equation:

-(4x^2+24x)


We get rid of parentheses

-4x^2+5x-24x-14=0

We add all the numbers together, and all the variables

-4x^2-19x-14=0

a = -4; b = -19; c = -14;
Δ = b2-4ac
Δ = -192-4·(-4)·(-14)
Δ = 137
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{137}}{2*-4}=\frac{19-\sqrt{137}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{137}}{2*-4}=\frac{19+\sqrt{137}}{-8}
$