-4.9x^2+4.5x+53=0

Solution for -4.9x^2+4.5x+53=0 equation:

-4.9x^2+4.5x+53=0

a = -4.9; b = 4.5; c = +53;
Δ = b2-4ac
Δ = 4.52-4·(-4.9)·53
Δ = 1059.05
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.5)-\sqrt{1059.05}}{2*-4.9}=\frac{-4.5-\sqrt{1059.05}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{1059.05}}{2*-4.9}=\frac{-4.5+\sqrt{1059.05}}{-9.8}
$