X(x-3)=10(4)

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

X(X-3)=10(4)

We move all terms to the left:

X(X-3)-(10(4))=0

determiningTheFunctionDomain
X(X-3)-104=0

We multiply parentheses

X^2-3X-104=0

a = 1; b = -3; c = -104;
Δ = b2-4ac
Δ = -32-4·1·(-104)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5\sqrt{17}}{2*1}=\frac{3-5\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5\sqrt{17}}{2*1}=\frac{3+5\sqrt{17}}{2}
$