4p^2-5p=10

Solution for 4p^2-5p=10 equation:

4p^2-5p=10

We move all terms to the left:

4p^2-5p-(10)=0

a = 4; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·4·(-10)
Δ = 185
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{-(-5)-\sqrt{185}}{2*4}=\frac{5-\sqrt{185}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*4}=\frac{5+\sqrt{185}}{8}
$