4x-3=7-x(x-8)

Solution for 4x-3=7-x(x-8) equation:

4x-3=7-x(x-8)

We move all terms to the left:

4x-3-(7-x(x-8))=0


We calculate terms in parentheses: -(7-x(x-8)), so:

7-x(x-8)

determiningTheFunctionDomain
-x(x-8)+7

We multiply parentheses

-x^2+8x+7

We add all the numbers together, and all the variables

-1x^2+8x+7

Back to the equation:

-(-1x^2+8x+7)


We get rid of parentheses

1x^2-8x+4x-7-3=0

We add all the numbers together, and all the variables

x^2-4x-10=0

a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2}
$