7p(-3p+4)=-2(2p-1)+10

Solution for 7p(-3p+4)=-2(2p-1)+10 equation:

7p(-3p+4)=-2(2p-1)+10

We move all terms to the left:

7p(-3p+4)-(-2(2p-1)+10)=0

We multiply parentheses

-21p^2+28p-(-2(2p-1)+10)=0


We calculate terms in parentheses: -(-2(2p-1)+10), so:

-2(2p-1)+10

We multiply parentheses

-4p+2+10

We add all the numbers together, and all the variables

-4p+12

Back to the equation:

-(-4p+12)


We get rid of parentheses

-21p^2+28p+4p-12=0

We add all the numbers together, and all the variables

-21p^2+32p-12=0

a = -21; b = 32; c = -12;
Δ = b2-4ac
Δ = 322-4·(-21)·(-12)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4}{2*-21}=\frac{-36}{-42}
=6/7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4}{2*-21}=\frac{-28}{-42}
=2/3
$