# 42x^2-11=14

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## Solution for 42x^2-11=14 equation:

42x^2-11=14
We move all terms to the left:
42x^2-11-(14)=0
We add all the numbers together, and all the variables
42x^2-25=0
a = 42; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·42·(-25)
Δ = 4200
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:
$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*42}=\frac{0-10\sqrt{42}}{84} =-\frac{10\sqrt{42}}{84} =-\frac{5\sqrt{42}}{42}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*42}=\frac{0+10\sqrt{42}}{84} =\frac{10\sqrt{42}}{84} =\frac{5\sqrt{42}}{42}$