9-x2/10=-19

Solution for 9-x2/10=-19 equation:

9-x2/10=-19

We move all terms to the left:

9-x2/10-(-19)=0

We add all the numbers together, and all the variables

-x2/10+28=0

We multiply all the terms by the denominator


-x2+28*10=0

We add all the numbers together, and all the variables

-1x^2+280=0

a = -1; b = 0; c = +280;
Δ = b2-4ac
Δ = 02-4·(-1)·280
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*-1}=\frac{0-4\sqrt{70}}{-2}
=-\frac{4\sqrt{70}}{-2}
=-\frac{2\sqrt{70}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*-1}=\frac{0+4\sqrt{70}}{-2}
=\frac{4\sqrt{70}}{-2}
=\frac{2\sqrt{70}}{-1}
$