(3x-16)(2x-7)=140+(x)(23-x)

Solution for (3x-16)(2x-7)=140+(x)(23-x) equation:

(3x-16)(2x-7)=140+(x)(23-x)

We move all terms to the left:

(3x-16)(2x-7)-(140+(x)(23-x))=0

We add all the numbers together, and all the variables

(3x-16)(2x-7)-(140+x(-1x+23))=0

We multiply parentheses ..

(+6x^2-21x-32x+112)-(140+x(-1x+23))=0


We calculate terms in parentheses: -(140+x(-1x+23)), so:

140+x(-1x+23)

determiningTheFunctionDomain
x(-1x+23)+140

We multiply parentheses

-1x^2+23x+140

Back to the equation:

-(-1x^2+23x+140)


We get rid of parentheses

6x^2+1x^2-21x-32x-23x+112-140=0

We add all the numbers together, and all the variables

7x^2-76x-28=0

a = 7; b = -76; c = -28;
Δ = b2-4ac
Δ = -762-4·7·(-28)
Δ = 6560
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:

$\sqrt{\Delta}=\sqrt{6560}=\sqrt{16*410}=\sqrt{16}*\sqrt{410}=4\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{410}}{2*7}=\frac{76-4\sqrt{410}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{410}}{2*7}=\frac{76+4\sqrt{410}}{14}
$