4x^2-8x=9

Solution for 4x^2-8x=9 equation:

4x^2-8x=9

We move all terms to the left:

4x^2-8x-(9)=0

a = 4; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·4·(-9)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*4}=\frac{8-4\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*4}=\frac{8+4\sqrt{13}}{8}
$