2c^2+2/10+9=19

Solution for 2c^2+2/10+9=19 equation:

2c^2+2/10+9=19

We move all terms to the left:

2c^2+2/10+9-(19)=0

determiningTheFunctionDomain
2c^2+9-19+2/10=0

We add all the numbers together, and all the variables

2c^2-10+2/10=0

We multiply all the terms by the denominator


2c^2*10+2-10*10=0

We add all the numbers together, and all the variables

2c^2*10-98=0

Wy multiply elements

20c^2-98=0

a = 20; b = 0; c = -98;
Δ = b2-4ac
Δ = 02-4·20·(-98)
Δ = 7840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7840}=\sqrt{784*10}=\sqrt{784}*\sqrt{10}=28\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{10}}{2*20}=\frac{0-28\sqrt{10}}{40}
=-\frac{28\sqrt{10}}{40}
=-\frac{7\sqrt{10}}{10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{10}}{2*20}=\frac{0+28\sqrt{10}}{40}
=\frac{28\sqrt{10}}{40}
=\frac{7\sqrt{10}}{10}
$