4*x^2+2*x-151=0

Solution for 4*x^2+2*x-151=0 equation:

4x^2+2x-151=0

a = 4; b = 2; c = -151;
Δ = b2-4ac
Δ = 22-4·4·(-151)
Δ = 2420
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:

$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22\sqrt{5}}{2*4}=\frac{-2-22\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22\sqrt{5}}{2*4}=\frac{-2+22\sqrt{5}}{8}
$