3x^2/5=42

Solution for 3x^2/5=42 equation:

3x^2/5=42

We move all terms to the left:

3x^2/5-(42)=0

We multiply all the terms by the denominator


3x^2-42*5=0

We add all the numbers together, and all the variables

3x^2-210=0

a = 3; b = 0; c = -210;
Δ = b2-4ac
Δ = 02-4·3·(-210)
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{70}}{2*3}=\frac{0-6\sqrt{70}}{6}
=-\frac{6\sqrt{70}}{6}
=-\sqrt{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{70}}{2*3}=\frac{0+6\sqrt{70}}{6}
=\frac{6\sqrt{70}}{6}
=\sqrt{70}
$