24x^2+34x=64

Solution for 24x^2+34x=64 equation:

24x^2+34x=64

We move all terms to the left:

24x^2+34x-(64)=0

a = 24; b = 34; c = -64;
Δ = b2-4ac
Δ = 342-4·24·(-64)
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-10\sqrt{73}}{2*24}=\frac{-34-10\sqrt{73}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+10\sqrt{73}}{2*24}=\frac{-34+10\sqrt{73}}{48}
$