4x^2+4V7x+7=0

Solution for 4x^2+4V7x+7=0 equation:

4x^2+47x+7=0

a = 4; b = 47; c = +7;
Δ = b2-4ac
Δ = 472-4·4·7
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-3\sqrt{233}}{2*4}=\frac{-47-3\sqrt{233}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+3\sqrt{233}}{2*4}=\frac{-47+3\sqrt{233}}{8}
$