3x^2+17=14x+9

Solution for 3x^2+17=14x+9 equation:

3x^2+17=14x+9

We move all terms to the left:

3x^2+17-(14x+9)=0

We get rid of parentheses

3x^2-14x-9+17=0

We add all the numbers together, and all the variables

3x^2-14x+8=0

a = 3; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·3·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*3}=\frac{24}{6}
=4
$