45x^2-11x-4=0

Solution for 45x^2-11x-4=0 equation:

45x^2-11x-4=0

a = 45; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·45·(-4)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*45}=\frac{-18}{90}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*45}=\frac{40}{90}
=4/9
$