4p^2-49=-21p

Solution for 4p^2-49=-21p equation:

4p^2-49=-21p

We move all terms to the left:

4p^2-49-(-21p)=0

We get rid of parentheses

4p^2+21p-49=0

a = 4; b = 21; c = -49;
Δ = b2-4ac
Δ = 212-4·4·(-49)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-35}{2*4}=\frac{-56}{8}
=-7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+35}{2*4}=\frac{14}{8}
=1+3/4
$