(5x-2=2x-11)-(3x^2+8x-7)

Solution for (5x-2=2x-11)-(3x^2+8x-7) equation:

(5x-2=2x-11)-(3x^2+8x-7)

We move all terms to the left:

(5x-2-(2x-11)-(3x^2+8x-7))=0


We calculate terms in parentheses: +(5x-2-(2x-11)-(3x^2+8x-7)), so:

5x-2-(2x-11)-(3x^2+8x-7)

determiningTheFunctionDomain
5x-(2x-11)-(3x^2+8x-7)-2

We get rid of parentheses

-3x^2+5x-2x-8x+11+7-2

We add all the numbers together, and all the variables

-3x^2-5x+16

Back to the equation:

+(-3x^2-5x+16)


We get rid of parentheses

-3x^2-5x+16=0

a = -3; b = -5; c = +16;
Δ = b2-4ac
Δ = -52-4·(-3)·16
Δ = 217
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{-(-5)-\sqrt{217}}{2*-3}=\frac{5-\sqrt{217}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*-3}=\frac{5+\sqrt{217}}{-6}
$