4-9x=3-10x(7-x)

Solution for 4-9x=3-10x(7-x) equation:

4-9x=3-10x(7-x)

We move all terms to the left:

4-9x-(3-10x(7-x))=0

We add all the numbers together, and all the variables

-9x-(3-10x(-1x+7))+4=0


We calculate terms in parentheses: -(3-10x(-1x+7)), so:

3-10x(-1x+7)

determiningTheFunctionDomain
-10x(-1x+7)+3

We multiply parentheses

10x^2-70x+3

Back to the equation:

-(10x^2-70x+3)


We get rid of parentheses

-10x^2-9x+70x-3+4=0

We add all the numbers together, and all the variables

-10x^2+61x+1=0

a = -10; b = 61; c = +1;
Δ = b2-4ac
Δ = 612-4·(-10)·1
Δ = 3761
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{-(61)-\sqrt{3761}}{2*-10}=\frac{-61-\sqrt{3761}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+\sqrt{3761}}{2*-10}=\frac{-61+\sqrt{3761}}{-20}
$