3x2+45=4x2+12x

Solution for 3x2+45=4x2+12x equation:

3x^2+45=4x^2+12x

We move all terms to the left:

3x^2+45-(4x^2+12x)=0

We get rid of parentheses

3x^2-4x^2-12x+45=0

We add all the numbers together, and all the variables

-1x^2-12x+45=0

a = -1; b = -12; c = +45;
Δ = b2-4ac
Δ = -122-4·(-1)·45
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*-1}=\frac{30}{-2}
=-15
$