3x^2+14=23x

Solution for 3x^2+14=23x equation:

3x^2+14=23x

We move all terms to the left:

3x^2+14-(23x)=0

a = 3; b = -23; c = +14;
Δ = b2-4ac
Δ = -232-4·3·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*3}=\frac{42}{6}
=7
$