10p^2=-6p+3

Solution for 10p^2=-6p+3 equation:

10p^2=-6p+3

We move all terms to the left:

10p^2-(-6p+3)=0

We get rid of parentheses

10p^2+6p-3=0

a = 10; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·10·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*10}=\frac{-6-2\sqrt{39}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*10}=\frac{-6+2\sqrt{39}}{20}
$