2p^2-17p=35

Solution for 2p^2-17p=35 equation:

2p^2-17p=35

We move all terms to the left:

2p^2-17p-(35)=0

a = 2; b = -17; c = -35;
Δ = b2-4ac
Δ = -172-4·2·(-35)
Δ = 569
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{-(-17)-\sqrt{569}}{2*2}=\frac{17-\sqrt{569}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{569}}{2*2}=\frac{17+\sqrt{569}}{4}
$