2,25x^2-111x+840=0

Solution for 2,25x^2-111x+840=0 equation:

2.25x^2-111x+840=0

a = 2.25; b = -111; c = +840;
Δ = b2-4ac
Δ = -1112-4·2.25·840
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-69}{2*2.25}=\frac{42}{4.5}
=9+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+69}{2*2.25}=\frac{180}{4.5}
=40
$