-9x2+42x-45=0

Solution for -9x2+42x-45=0 equation:

-9x^2+42x-45=0

a = -9; b = 42; c = -45;
Δ = b2-4ac
Δ = 422-4·(-9)·(-45)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-12}{2*-9}=\frac{-54}{-18}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+12}{2*-9}=\frac{-30}{-18}
=1+2/3
$