10x^2-20=9

Solution for 10x^2-20=9 equation:

10x^2-20=9

We move all terms to the left:

10x^2-20-(9)=0

We add all the numbers together, and all the variables

10x^2-29=0

a = 10; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·10·(-29)
Δ = 1160
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:

$\sqrt{\Delta}=\sqrt{1160}=\sqrt{4*290}=\sqrt{4}*\sqrt{290}=2\sqrt{290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{290}}{2*10}=\frac{0-2\sqrt{290}}{20}
=-\frac{2\sqrt{290}}{20}
=-\frac{\sqrt{290}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{290}}{2*10}=\frac{0+2\sqrt{290}}{20}
=\frac{2\sqrt{290}}{20}
=\frac{\sqrt{290}}{10}
$