6p^2=8p+3

Solution for 6p^2=8p+3 equation:

6p^2=8p+3

We move all terms to the left:

6p^2-(8p+3)=0

We get rid of parentheses

6p^2-8p-3=0

a = 6; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·6·(-3)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*6}=\frac{8-2\sqrt{34}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*6}=\frac{8+2\sqrt{34}}{12}
$