(x-7,5)(2x-3)=57,5

Solution for (x-7,5)(2x-3)=57,5 equation:

(x-7.5)(2x-3)=57.5

We move all terms to the left:

(x-7.5)(2x-3)-(57.5)=0

We add all the numbers together, and all the variables

(x-7.5)(2x-3)-57.5=0

We multiply parentheses ..

(+2x^2-3x-15x+22.5)-57.5=0

We get rid of parentheses

2x^2-3x-15x+22.5-57.5=0

We add all the numbers together, and all the variables

2x^2-18x-35=0

a = 2; b = -18; c = -35;
Δ = b2-4ac
Δ = -182-4·2·(-35)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{151}}{2*2}=\frac{18-2\sqrt{151}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{151}}{2*2}=\frac{18+2\sqrt{151}}{4}
$