7x(25-x)-5x=2(3x-25)-3x

Solution for 7x(25-x)-5x=2(3x-25)-3x equation:

7x(25-x)-5x=2(3x-25)-3x

We move all terms to the left:

7x(25-x)-5x-(2(3x-25)-3x)=0

We add all the numbers together, and all the variables

7x(-1x+25)-5x-(2(3x-25)-3x)=0

We add all the numbers together, and all the variables

-5x+7x(-1x+25)-(2(3x-25)-3x)=0

We multiply parentheses

-7x^2-5x+175x-(2(3x-25)-3x)=0


We calculate terms in parentheses: -(2(3x-25)-3x), so:

2(3x-25)-3x

We add all the numbers together, and all the variables

-3x+2(3x-25)

We multiply parentheses

-3x+6x-50

We add all the numbers together, and all the variables

3x-50

Back to the equation:

-(3x-50)


We add all the numbers together, and all the variables

-7x^2+170x-(3x-50)=0

We get rid of parentheses

-7x^2+170x-3x+50=0

We add all the numbers together, and all the variables

-7x^2+167x+50=0

a = -7; b = 167; c = +50;
Δ = b2-4ac
Δ = 1672-4·(-7)·50
Δ = 29289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(167)-\sqrt{29289}}{2*-7}=\frac{-167-\sqrt{29289}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(167)+\sqrt{29289}}{2*-7}=\frac{-167+\sqrt{29289}}{-14}
$