10x^2+9=456

Solution for 10x^2+9=456 equation:

10x^2+9=456

We move all terms to the left:

10x^2+9-(456)=0

We add all the numbers together, and all the variables

10x^2-447=0

a = 10; b = 0; c = -447;
Δ = b2-4ac
Δ = 02-4·10·(-447)
Δ = 17880
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:

$\sqrt{\Delta}=\sqrt{17880}=\sqrt{4*4470}=\sqrt{4}*\sqrt{4470}=2\sqrt{4470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4470}}{2*10}=\frac{0-2\sqrt{4470}}{20}
=-\frac{2\sqrt{4470}}{20}
=-\frac{\sqrt{4470}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4470}}{2*10}=\frac{0+2\sqrt{4470}}{20}
=\frac{2\sqrt{4470}}{20}
=\frac{\sqrt{4470}}{10}
$