4X2+2x-25=0

Solution for 4X2+2x-25=0 equation:

4X^2+2X-25=0

a = 4; b = 2; c = -25;
Δ = b2-4ac
Δ = 22-4·4·(-25)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{101}}{2*4}=\frac{-2-2\sqrt{101}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{101}}{2*4}=\frac{-2+2\sqrt{101}}{8}
$