101-2x=(2x+3)(x+2)

Solution for 101-2x=(2x+3)(x+2) equation:

101-2x=(2x+3)(x+2)

We move all terms to the left:

101-2x-((2x+3)(x+2))=0

We multiply parentheses ..

-((+2x^2+4x+3x+6))-2x+101=0


We calculate terms in parentheses: -((+2x^2+4x+3x+6)), so:

(+2x^2+4x+3x+6)

We get rid of parentheses

2x^2+4x+3x+6

We add all the numbers together, and all the variables

2x^2+7x+6

Back to the equation:

-(2x^2+7x+6)


We add all the numbers together, and all the variables

-2x-(2x^2+7x+6)+101=0

We get rid of parentheses

-2x^2-2x-7x-6+101=0

We add all the numbers together, and all the variables

-2x^2-9x+95=0

a = -2; b = -9; c = +95;
Δ = b2-4ac
Δ = -92-4·(-2)·95
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-29}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+29}{2*-2}=\frac{38}{-4}
=-9+1/2
$