(5p+3)(2p-7)=37

Solution for (5p+3)(2p-7)=37 equation:

(5p+3)(2p-7)=37

We move all terms to the left:

(5p+3)(2p-7)-(37)=0

We multiply parentheses ..

(+10p^2-35p+6p-21)-37=0

We get rid of parentheses

10p^2-35p+6p-21-37=0

We add all the numbers together, and all the variables

10p^2-29p-58=0

a = 10; b = -29; c = -58;
Δ = b2-4ac
Δ = -292-4·10·(-58)
Δ = 3161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{3161}}{2*10}=\frac{29-\sqrt{3161}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{3161}}{2*10}=\frac{29+\sqrt{3161}}{20}
$