x(x-8)+(x-2)(x-3)=1.75

Solution for x(x-8)+(x-2)(x-3)=1.75 equation:

x(x-8)+(x-2)(x-3)=1.75

We move all terms to the left:

x(x-8)+(x-2)(x-3)-(1.75)=0

We add all the numbers together, and all the variables

x(x-8)+(x-2)(x-3)-1.75=0

We multiply parentheses

x^2-8x+(x-2)(x-3)-1.75=0

We multiply parentheses ..

x^2+(+x^2-3x-2x+6)-8x-1.75=0

We get rid of parentheses

x^2+x^2-3x-2x-8x+6-1.75=0

We add all the numbers together, and all the variables

2x^2-13x+4.25=0

a = 2; b = -13; c = +4.25;
Δ = b2-4ac
Δ = -132-4·2·4.25
Δ = 135
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:

$\sqrt{\Delta}=\sqrt{135}=\sqrt{9*15}=\sqrt{9}*\sqrt{15}=3\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{15}}{2*2}=\frac{13-3\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{15}}{2*2}=\frac{13+3\sqrt{15}}{4}
$