4x^2-100x-3=0

Solution for 4x^2-100x-3=0 equation:

4x^2-100x-3=0

a = 4; b = -100; c = -3;
Δ = b2-4ac
Δ = -1002-4·4·(-3)
Δ = 10048
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:

$\sqrt{\Delta}=\sqrt{10048}=\sqrt{64*157}=\sqrt{64}*\sqrt{157}=8\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-8\sqrt{157}}{2*4}=\frac{100-8\sqrt{157}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+8\sqrt{157}}{2*4}=\frac{100+8\sqrt{157}}{8}
$