3x^2-42=15x

Solution for 3x^2-42=15x equation:

3x^2-42=15x

We move all terms to the left:

3x^2-42-(15x)=0

a = 3; b = -15; c = -42;
Δ = b2-4ac
Δ = -152-4·3·(-42)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-27}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+27}{2*3}=\frac{42}{6}
=7
$