(9-2x)(5-x)=10

Solution for (9-2x)(5-x)=10 equation:

(9-2x)(5-x)=10

We move all terms to the left:

(9-2x)(5-x)-(10)=0

We add all the numbers together, and all the variables

(-2x+9)(-1x+5)-10=0

We multiply parentheses ..

(+2x^2-10x-9x+45)-10=0

We get rid of parentheses

2x^2-10x-9x+45-10=0

We add all the numbers together, and all the variables

2x^2-19x+35=0

a = 2; b = -19; c = +35;
Δ = b2-4ac
Δ = -192-4·2·35
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-9}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+9}{2*2}=\frac{28}{4}
=7
$