7p^2-38p+3=0

Solution for 7p^2-38p+3=0 equation:

7p^2-38p+3=0

a = 7; b = -38; c = +3;
Δ = b2-4ac
Δ = -382-4·7·3
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-4\sqrt{85}}{2*7}=\frac{38-4\sqrt{85}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+4\sqrt{85}}{2*7}=\frac{38+4\sqrt{85}}{14}
$