9-5x2=10x

Solution for 9-5x2=10x equation:

9-5x^2=10x

We move all terms to the left:

9-5x^2-(10x)=0

a = -5; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·(-5)·9
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*-5}=\frac{10-2\sqrt{70}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*-5}=\frac{10+2\sqrt{70}}{-10}
$