14x^2=24x+54

Solution for 14x^2=24x+54 equation:

14x^2=24x+54

We move all terms to the left:

14x^2-(24x+54)=0

We get rid of parentheses

14x^2-24x-54=0

a = 14; b = -24; c = -54;
Δ = b2-4ac
Δ = -242-4·14·(-54)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-60}{2*14}=\frac{-36}{28}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+60}{2*14}=\frac{84}{28}
=3
$