7p^2-4p=40-3p^2

Solution for 7p^2-4p=40-3p^2 equation:

7p^2-4p=40-3p^2

We move all terms to the left:

7p^2-4p-(40-3p^2)=0

We get rid of parentheses

7p^2+3p^2-4p-40=0

We add all the numbers together, and all the variables

10p^2-4p-40=0

a = 10; b = -4; c = -40;
Δ = b2-4ac
Δ = -42-4·10·(-40)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{101}}{2*10}=\frac{4-4\sqrt{101}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{101}}{2*10}=\frac{4+4\sqrt{101}}{20}
$