6x^2-29x=5x-48

Solution for 6x^2-29x=5x-48 equation:

6x^2-29x=5x-48

We move all terms to the left:

6x^2-29x-(5x-48)=0

We get rid of parentheses

6x^2-29x-5x+48=0

We add all the numbers together, and all the variables

6x^2-34x+48=0

a = 6; b = -34; c = +48;
Δ = b2-4ac
Δ = -342-4·6·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*6}=\frac{32}{12}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*6}=\frac{36}{12}
=3
$