7x^2-5-2x-3=6-(2x+3)=

Solution for 7x^2-5-2x-3=6-(2x+3)= equation:

7x^2-5-2x-3=6-(2x+3)=

We move all terms to the left:

7x^2-5-2x-3-(6-(2x+3))=0

We add all the numbers together, and all the variables

7x^2-2x-(6-(2x+3))-8=0


We calculate terms in parentheses: -(6-(2x+3)), so:

6-(2x+3)

determiningTheFunctionDomain
-(2x+3)+6

We get rid of parentheses

-2x-3+6

We add all the numbers together, and all the variables

-2x+3

Back to the equation:

-(-2x+3)


We get rid of parentheses

7x^2-2x+2x-3-8=0

We add all the numbers together, and all the variables

7x^2-11=0

a = 7; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·7·(-11)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*7}=\frac{0-2\sqrt{77}}{14}
=-\frac{2\sqrt{77}}{14}
=-\frac{\sqrt{77}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*7}=\frac{0+2\sqrt{77}}{14}
=\frac{2\sqrt{77}}{14}
=\frac{\sqrt{77}}{7}
$