3(4p+1)=7(p+9)34p+1=7(p+9)

Solution for 3(4p+1)=7(p+9)34p+1=7(p+9) equation:

3(4p+1)=7(p+9)34p+1=7(p+9)

We move all terms to the left:

3(4p+1)-(7(p+9)34p+1)=0

We multiply parentheses

12p-(7(p+9)34p+1)+3=0


We calculate terms in parentheses: -(7(p+9)34p+1), so:

7(p+9)34p+1

We multiply parentheses

238p^2+2142p+1

Back to the equation:

-(238p^2+2142p+1)


We get rid of parentheses

-238p^2+12p-2142p-1+3=0

We add all the numbers together, and all the variables

-238p^2-2130p+2=0

a = -238; b = -2130; c = +2;
Δ = b2-4ac
Δ = -21302-4·(-238)·2
Δ = 4538804
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:

$\sqrt{\Delta}=\sqrt{4538804}=\sqrt{4*1134701}=\sqrt{4}*\sqrt{1134701}=2\sqrt{1134701}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2130)-2\sqrt{1134701}}{2*-238}=\frac{2130-2\sqrt{1134701}}{-476}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2130)+2\sqrt{1134701}}{2*-238}=\frac{2130+2\sqrt{1134701}}{-476}
$