X^2=10x+9=0

Solution for X^2=10x+9=0 equation:

X^2=10X+9=0

We move all terms to the left:

X^2-(10X+9)=0

We get rid of parentheses

X^2-10X-9=0

a = 1; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·1·(-9)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{34}}{2*1}=\frac{10-2\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{34}}{2*1}=\frac{10+2\sqrt{34}}{2}
$