x^2-5x+30=12x

Solution for x^2-5x+30=12x equation:

x^2-5x+30=12x

We move all terms to the left:

x^2-5x+30-(12x)=0

We add all the numbers together, and all the variables

x^2-17x+30=0

a = 1; b = -17; c = +30;
Δ = b2-4ac
Δ = -172-4·1·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*1}=\frac{30}{2}
=15
$