17u-6=5u^2

Solution for 17u-6=5u^2 equation:

17u-6=5u^2

We move all terms to the left:

17u-6-(5u^2)=0

determiningTheFunctionDomain
-5u^2+17u-6=0

a = -5; b = 17; c = -6;
Δ = b2-4ac
Δ = 172-4·(-5)·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*-5}=\frac{-30}{-10}
=+3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*-5}=\frac{-4}{-10}
=2/5
$