2x-5*3=7*5-(x*x-5)

Solution for 2x-5*3=7*5-(x*x-5) equation:

2x-5*3=7*5-(x*x-5)

We move all terms to the left:

2x-5*3-(7*5-(x*x-5))=0

We add all the numbers together, and all the variables

2x-(7*5-(x*x-5))-15=0


We calculate terms in parentheses: -(7*5-(x*x-5)), so:

7*5-(x*x-5)

determiningTheFunctionDomain
-(x*x-5)+7*5

We add all the numbers together, and all the variables

-(x*x-5)+35

We get rid of parentheses

-x*x+5+35

We add all the numbers together, and all the variables

-x*x+40

Wy multiply elements

-1x^2+40

Back to the equation:

-(-1x^2+40)


We get rid of parentheses

1x^2+2x-40-15=0

We add all the numbers together, and all the variables

x^2+2x-55=0

a = 1; b = 2; c = -55;
Δ = b2-4ac
Δ = 22-4·1·(-55)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{14}}{2*1}=\frac{-2-4\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{14}}{2*1}=\frac{-2+4\sqrt{14}}{2}
$