42x=7x^2

Solution for 42x=7x^2 equation:

42x=7x^2

We move all terms to the left:

42x-(7x^2)=0

determiningTheFunctionDomain
-7x^2+42x=0

a = -7; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-7)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-7}=\frac{-84}{-14}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-7}=\frac{0}{-14}
=0
$