975=(19-2x)(23-2x)

Solution for 975=(19-2x)(23-2x) equation:

975=(19-2x)(23-2x)

We move all terms to the left:

975-((19-2x)(23-2x))=0

We add all the numbers together, and all the variables

-((-2x+19)(-2x+23))+975=0

We multiply parentheses ..

-((+4x^2-46x-38x+437))+975=0


We calculate terms in parentheses: -((+4x^2-46x-38x+437)), so:

(+4x^2-46x-38x+437)

We get rid of parentheses

4x^2-46x-38x+437

We add all the numbers together, and all the variables

4x^2-84x+437

Back to the equation:

-(4x^2-84x+437)


We get rid of parentheses

-4x^2+84x-437+975=0

We add all the numbers together, and all the variables

-4x^2+84x+538=0

a = -4; b = 84; c = +538;
Δ = b2-4ac
Δ = 842-4·(-4)·538
Δ = 15664
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:

$\sqrt{\Delta}=\sqrt{15664}=\sqrt{16*979}=\sqrt{16}*\sqrt{979}=4\sqrt{979}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{979}}{2*-4}=\frac{-84-4\sqrt{979}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{979}}{2*-4}=\frac{-84+4\sqrt{979}}{-8}
$