x-15=7-5(x-4)x=

Solution for x-15=7-5(x-4)x= equation:

x-15=7-5(x-4)x=

We move all terms to the left:

x-15-(7-5(x-4)x)=0


We calculate terms in parentheses: -(7-5(x-4)x), so:

7-5(x-4)x

determiningTheFunctionDomain
-5(x-4)x+7

We multiply parentheses

-5x^2+20x+7

Back to the equation:

-(-5x^2+20x+7)


We get rid of parentheses

5x^2-20x+x-7-15=0

We add all the numbers together, and all the variables

5x^2-19x-22=0

a = 5; b = -19; c = -22;
Δ = b2-4ac
Δ = -192-4·5·(-22)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{89}}{2*5}=\frac{19-3\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{89}}{2*5}=\frac{19+3\sqrt{89}}{10}
$