6x^2-84x+272=3x^2-48x+167

Solution for 6x^2-84x+272=3x^2-48x+167 equation:

6x^2-84x+272=3x^2-48x+167

We move all terms to the left:

6x^2-84x+272-(3x^2-48x+167)=0

We get rid of parentheses

6x^2-3x^2-84x+48x-167+272=0

We add all the numbers together, and all the variables

3x^2-36x+105=0

a = 3; b = -36; c = +105;
Δ = b2-4ac
Δ = -362-4·3·105
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6}{2*3}=\frac{30}{6}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6}{2*3}=\frac{42}{6}
=7
$