7x^2+153/200=5

Solution for 7x^2+153/200=5 equation:

7x^2+153/200=5

We move all terms to the left:

7x^2+153/200-(5)=0

determiningTheFunctionDomain
7x^2-5+153/200=0

We multiply all the terms by the denominator


7x^2*200+153-5*200=0

We add all the numbers together, and all the variables

7x^2*200-847=0

Wy multiply elements

1400x^2-847=0

a = 1400; b = 0; c = -847;
Δ = b2-4ac
Δ = 02-4·1400·(-847)
Δ = 4743200
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:

$\sqrt{\Delta}=\sqrt{4743200}=\sqrt{2371600*2}=\sqrt{2371600}*\sqrt{2}=1540\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1540\sqrt{2}}{2*1400}=\frac{0-1540\sqrt{2}}{2800}
=-\frac{1540\sqrt{2}}{2800}
=-\frac{11\sqrt{2}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1540\sqrt{2}}{2*1400}=\frac{0+1540\sqrt{2}}{2800}
=\frac{1540\sqrt{2}}{2800}
=\frac{11\sqrt{2}}{20}
$