x^2-9x=5670

Solution for x^2-9x=5670 equation:

x^2-9x=5670

We move all terms to the left:

x^2-9x-(5670)=0

a = 1; b = -9; c = -5670;
Δ = b2-4ac
Δ = -92-4·1·(-5670)
Δ = 22761
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:

$\sqrt{\Delta}=\sqrt{22761}=\sqrt{81*281}=\sqrt{81}*\sqrt{281}=9\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{281}}{2*1}=\frac{9-9\sqrt{281}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{281}}{2*1}=\frac{9+9\sqrt{281}}{2}
$