24x^2+198x+243=0

Solution for 24x^2+198x+243=0 equation:

24x^2+198x+243=0

a = 24; b = 198; c = +243;
Δ = b2-4ac
Δ = 1982-4·24·243
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-126}{2*24}=\frac{-324}{48}
=-6+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+126}{2*24}=\frac{-72}{48}
=-1+1/2
$