8x^2-45x=24

Solution for 8x^2-45x=24 equation:

8x^2-45x=24

We move all terms to the left:

8x^2-45x-(24)=0

a = 8; b = -45; c = -24;
Δ = b2-4ac
Δ = -452-4·8·(-24)
Δ = 2793
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:

$\sqrt{\Delta}=\sqrt{2793}=\sqrt{49*57}=\sqrt{49}*\sqrt{57}=7\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-7\sqrt{57}}{2*8}=\frac{45-7\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+7\sqrt{57}}{2*8}=\frac{45+7\sqrt{57}}{16}
$