6p^2=-5p+13

Solution for 6p^2=-5p+13 equation:

6p^2=-5p+13

We move all terms to the left:

6p^2-(-5p+13)=0

We get rid of parentheses

6p^2+5p-13=0

a = 6; b = 5; c = -13;
Δ = b2-4ac
Δ = 52-4·6·(-13)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{337}}{2*6}=\frac{-5-\sqrt{337}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{337}}{2*6}=\frac{-5+\sqrt{337}}{12}
$