X*3x+42=102

Solution for X*3x+42=102 equation:

X*3X+42=102

We move all terms to the left:

X*3X+42-(102)=0

We add all the numbers together, and all the variables

X*3X-60=0

Wy multiply elements

3X^2-60=0

a = 3; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·3·(-60)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*3}=\frac{0-12\sqrt{5}}{6}
=-\frac{12\sqrt{5}}{6}
=-2\sqrt{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*3}=\frac{0+12\sqrt{5}}{6}
=\frac{12\sqrt{5}}{6}
=2\sqrt{5}
$