6x-3x(5-x)=10-(x+7)(2x-5)

Solution for 6x-3x(5-x)=10-(x+7)(2x-5) equation:

6x-3x(5-x)=10-(x+7)(2x-5)

We move all terms to the left:

6x-3x(5-x)-(10-(x+7)(2x-5))=0

We add all the numbers together, and all the variables

6x-3x(-1x+5)-(10-(x+7)(2x-5))=0

We multiply parentheses

3x^2+6x-15x-(10-(x+7)(2x-5))=0

We multiply parentheses ..

3x^2-(10-(+2x^2-5x+14x-35))+6x-15x=0


We calculate terms in parentheses: -(10-(+2x^2-5x+14x-35)), so:

10-(+2x^2-5x+14x-35)

determiningTheFunctionDomain
-(+2x^2-5x+14x-35)+10

We get rid of parentheses

-2x^2+5x-14x+35+10

We add all the numbers together, and all the variables

-2x^2-9x+45

Back to the equation:

-(-2x^2-9x+45)


We add all the numbers together, and all the variables

3x^2-(-2x^2-9x+45)-9x=0

We get rid of parentheses

3x^2+2x^2+9x-9x-45=0

We add all the numbers together, and all the variables

5x^2-45=0

a = 5; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·5·(-45)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*5}=\frac{30}{10}
=3
$