5p^2=114-11p

Solution for 5p^2=114-11p equation:

5p^2=114-11p

We move all terms to the left:

5p^2-(114-11p)=0

We add all the numbers together, and all the variables

5p^2-(-11p+114)=0

We get rid of parentheses

5p^2+11p-114=0

a = 5; b = 11; c = -114;
Δ = b2-4ac
Δ = 112-4·5·(-114)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-49}{2*5}=\frac{-60}{10}
=-6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+49}{2*5}=\frac{38}{10}
=3+4/5
$