(23-2x)(15-2x)=172,5

Solution for (23-2x)(15-2x)=172,5 equation:

(23-2x)(15-2x)=172.5

We move all terms to the left:

(23-2x)(15-2x)-(172.5)=0

We add all the numbers together, and all the variables

(-2x+23)(-2x+15)-(172.5)=0

We add all the numbers together, and all the variables

(-2x+23)(-2x+15)-172.5=0

We multiply parentheses ..

(+4x^2-30x-46x+345)-172.5=0

We get rid of parentheses

4x^2-30x-46x+345-172.5=0

We add all the numbers together, and all the variables

4x^2-76x+172.5=0

a = 4; b = -76; c = +172.5;
Δ = b2-4ac
Δ = -762-4·4·172.5
Δ = 3016
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:

$\sqrt{\Delta}=\sqrt{3016}=\sqrt{4*754}=\sqrt{4}*\sqrt{754}=2\sqrt{754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{754}}{2*4}=\frac{76-2\sqrt{754}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{754}}{2*4}=\frac{76+2\sqrt{754}}{8}
$