6x^2+5=4x+47

Solution for 6x^2+5=4x+47 equation:

6x^2+5=4x+47

We move all terms to the left:

6x^2+5-(4x+47)=0

We get rid of parentheses

6x^2-4x-47+5=0

We add all the numbers together, and all the variables

6x^2-4x-42=0

a = 6; b = -4; c = -42;
Δ = b2-4ac
Δ = -42-4·6·(-42)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*6}=\frac{36}{12}
=3
$