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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

(x^2-3x+6)

We get rid of parentheses

x^2-3x+6

Back to the equation:

-(x^2-3x+6)


We get rid of parentheses

-x^2+5x+3x-6+2=0

We add all the numbers together, and all the variables

-1x^2+8x-4=0

a = -1; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·(-1)·(-4)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3}}{2*-1}=\frac{-8-4\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3}}{2*-1}=\frac{-8+4\sqrt{3}}{-2}
$