(5x^2-8x+12)+(-5=15x-3x^2)

Solution for (5x^2-8x+12)+(-5=15x-3x^2) equation:

(5x^2-8x+12)+(-5=15x-3x^2)

We move all terms to the left:

(5x^2-8x+12)+(-5-(15x-3x^2))=0

We get rid of parentheses

(-5-(15x-3x^2))+5x^2-8x+12=0


We calculate terms in parentheses: +(-5-(15x-3x^2)), so:

-5-(15x-3x^2)

determiningTheFunctionDomain
-(15x-3x^2)-5

We get rid of parentheses

3x^2-15x-5

Back to the equation:

+(3x^2-15x-5)


We add all the numbers together, and all the variables

5x^2-8x+(3x^2-15x-5)+12=0

We get rid of parentheses

5x^2+3x^2-8x-15x-5+12=0

We add all the numbers together, and all the variables

8x^2-23x+7=0

a = 8; b = -23; c = +7;
Δ = b2-4ac
Δ = -232-4·8·7
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{305}}{2*8}=\frac{23-\sqrt{305}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{305}}{2*8}=\frac{23+\sqrt{305}}{16}
$