(X-4)(x+1)=10.25

Solution for (X-4)(x+1)=10.25 equation:

(X-4)(X+1)=10.25

We move all terms to the left:

(X-4)(X+1)-(10.25)=0

We add all the numbers together, and all the variables

(X-4)(X+1)-10.25=0

We multiply parentheses ..

(+X^2+X-4X-4)-10.25=0

We get rid of parentheses

X^2+X-4X-4-10.25=0

We add all the numbers together, and all the variables

X^2-3X-14.25=0

a = 1; b = -3; c = -14.25;
Δ = b2-4ac
Δ = -32-4·1·(-14.25)
Δ = 66
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{-(-3)-\sqrt{66}}{2*1}=\frac{3-\sqrt{66}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{66}}{2*1}=\frac{3+\sqrt{66}}{2}
$