P(x)=3x2-5x+1L(x)=x2-7x-3P(x)+L(x)=

Solution for P(x)=3x2-5x+1L(x)=x2-7x-3P(x)+L(x)= equation:

(P)=3P^2-5P+1(P)=P2-7P-3(P)+(P)=

We move all terms to the left:

(P)-(3P^2-5P+1(P))=0

We get rid of parentheses

-3P^2+P+5P-1P=0

We add all the numbers together, and all the variables

-3P^2+5P=0

a = -3; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-3)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-3}=\frac{0}{-6}
=0
$