3x^2-42x+147=29

Solution for 3x^2-42x+147=29 equation:

3x^2-42x+147=29

We move all terms to the left:

3x^2-42x+147-(29)=0

We add all the numbers together, and all the variables

3x^2-42x+118=0

a = 3; b = -42; c = +118;
Δ = b2-4ac
Δ = -422-4·3·118
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{87}}{2*3}=\frac{42-2\sqrt{87}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{87}}{2*3}=\frac{42+2\sqrt{87}}{6}
$