40=25+4x(x-6)

Solution for 40=25+4x(x-6) equation:

40=25+4x(x-6)

We move all terms to the left:

40-(25+4x(x-6))=0


We calculate terms in parentheses: -(25+4x(x-6)), so:

25+4x(x-6)

determiningTheFunctionDomain
4x(x-6)+25

We multiply parentheses

4x^2-24x+25

Back to the equation:

-(4x^2-24x+25)


We get rid of parentheses

-4x^2+24x-25+40=0

We add all the numbers together, and all the variables

-4x^2+24x+15=0

a = -4; b = 24; c = +15;
Δ = b2-4ac
Δ = 242-4·(-4)·15
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{51}}{2*-4}=\frac{-24-4\sqrt{51}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{51}}{2*-4}=\frac{-24+4\sqrt{51}}{-8}
$