30+2x^2=17x

Solution for 30+2x^2=17x equation:

30+2x^2=17x

We move all terms to the left:

30+2x^2-(17x)=0

a = 2; b = -17; c = +30;
Δ = b2-4ac
Δ = -172-4·2·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*2}=\frac{24}{4}
=6
$