3x(x-5)=20-(4x-3)

Solution for 3x(x-5)=20-(4x-3) equation:

3x(x-5)=20-(4x-3)

We move all terms to the left:

3x(x-5)-(20-(4x-3))=0

We multiply parentheses

3x^2-15x-(20-(4x-3))=0


We calculate terms in parentheses: -(20-(4x-3)), so:

20-(4x-3)

determiningTheFunctionDomain
-(4x-3)+20

We get rid of parentheses

-4x+3+20

We add all the numbers together, and all the variables

-4x+23

Back to the equation:

-(-4x+23)


We get rid of parentheses

3x^2-15x+4x-23=0

We add all the numbers together, and all the variables

3x^2-11x-23=0

a = 3; b = -11; c = -23;
Δ = b2-4ac
Δ = -112-4·3·(-23)
Δ = 397
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{-(-11)-\sqrt{397}}{2*3}=\frac{11-\sqrt{397}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{397}}{2*3}=\frac{11+\sqrt{397}}{6}
$