10-x^2=-27

Solution for 10-x^2=-27 equation:

10-x^2=-27

We move all terms to the left:

10-x^2-(-27)=0

We add all the numbers together, and all the variables

-1x^2+37=0

a = -1; b = 0; c = +37;
Δ = b2-4ac
Δ = 02-4·(-1)·37
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{37}}{2*-1}=\frac{0-2\sqrt{37}}{-2}
=-\frac{2\sqrt{37}}{-2}
=-\frac{\sqrt{37}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{37}}{2*-1}=\frac{0+2\sqrt{37}}{-2}
=\frac{2\sqrt{37}}{-2}
=\frac{\sqrt{37}}{-1}
$