6p^2=47p-35

Solution for 6p^2=47p-35 equation:

6p^2=47p-35

We move all terms to the left:

6p^2-(47p-35)=0

We get rid of parentheses

6p^2-47p+35=0

a = 6; b = -47; c = +35;
Δ = b2-4ac
Δ = -472-4·6·35
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-37}{2*6}=\frac{10}{12}
=5/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+37}{2*6}=\frac{84}{12}
=7
$