4p2+7=335

Solution for 4p2+7=335 equation:

4p^2+7=335

We move all terms to the left:

4p^2+7-(335)=0

We add all the numbers together, and all the variables

4p^2-328=0

a = 4; b = 0; c = -328;
Δ = b2-4ac
Δ = 02-4·4·(-328)
Δ = 5248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5248}=\sqrt{64*82}=\sqrt{64}*\sqrt{82}=8\sqrt{82}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{82}}{2*4}=\frac{0-8\sqrt{82}}{8}
=-\frac{8\sqrt{82}}{8}
=-\sqrt{82}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{82}}{2*4}=\frac{0+8\sqrt{82}}{8}
=\frac{8\sqrt{82}}{8}
=\sqrt{82}
$