16x2+24x=100

Solution for 16x2+24x=100 equation:

16x^2+24x=100

We move all terms to the left:

16x^2+24x-(100)=0

a = 16; b = 24; c = -100;
Δ = b2-4ac
Δ = 242-4·16·(-100)
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{109}}{2*16}=\frac{-24-8\sqrt{109}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{109}}{2*16}=\frac{-24+8\sqrt{109}}{32}
$