10x^2-20x-60=9

Solution for 10x^2-20x-60=9 equation:

10x^2-20x-60=9

We move all terms to the left:

10x^2-20x-60-(9)=0

We add all the numbers together, and all the variables

10x^2-20x-69=0

a = 10; b = -20; c = -69;
Δ = b2-4ac
Δ = -202-4·10·(-69)
Δ = 3160
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:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{790}}{2*10}=\frac{20-2\sqrt{790}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{790}}{2*10}=\frac{20+2\sqrt{790}}{20}
$