-3x^2=15x-42

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

-3x^2=15x-42

We move all terms to the left:

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

We get rid of parentheses

-3x^2-15x+42=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
$