6p^2+10p=23

Solution for 6p^2+10p=23 equation:

6p^2+10p=23

We move all terms to the left:

6p^2+10p-(23)=0

a = 6; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·6·(-23)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{163}}{2*6}=\frac{-10-2\sqrt{163}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{163}}{2*6}=\frac{-10+2\sqrt{163}}{12}
$