6x(4x+5)=54

Solution for 6x(4x+5)=54 equation:

6x(4x+5)=54

We move all terms to the left:

6x(4x+5)-(54)=0

We multiply parentheses

24x^2+30x-54=0

a = 24; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·24·(-54)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-78}{2*24}=\frac{-108}{48}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+78}{2*24}=\frac{48}{48}
=1
$