4p2+19p-53=9p-3

Solution for 4p2+19p-53=9p-3 equation:

4p^2+19p-53=9p-3

We move all terms to the left:

4p^2+19p-53-(9p-3)=0

We get rid of parentheses

4p^2+19p-9p+3-53=0

We add all the numbers together, and all the variables

4p^2+10p-50=0

a = 4; b = 10; c = -50;
Δ = b2-4ac
Δ = 102-4·4·(-50)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*4}=\frac{-40}{8}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*4}=\frac{20}{8}
=2+1/2
$