10x-4.9x^2=-45

Solution for 10x-4.9x^2=-45 equation:

10x-4.9x^2=-45

We move all terms to the left:

10x-4.9x^2-(-45)=0

We add all the numbers together, and all the variables

-4.9x^2+10x+45=0

a = -4.9; b = 10; c = +45;
Δ = b2-4ac
Δ = 102-4·(-4.9)·45
Δ = 982
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{982}=\sqrt{1*982}=\sqrt{1}*\sqrt{982}=1\sqrt{982}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-1\sqrt{982}}{2*-4.9}=\frac{-10-1\sqrt{982}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+1\sqrt{982}}{2*-4.9}=\frac{-10+1\sqrt{982}}{-9.8}
$