-0.5=(x+4)(x-2.5)

Solution for -0.5=(x+4)(x-2.5) equation:

-0.5=(x+4)(x-2.5)

We move all terms to the left:

-0.5-((x+4)(x-2.5))=0

We multiply parentheses ..

-((+x^2-2.5x+4x-10))-0.5=0


We calculate terms in parentheses: -((+x^2-2.5x+4x-10)), so:

(+x^2-2.5x+4x-10)

We get rid of parentheses

x^2-2.5x+4x-10

We add all the numbers together, and all the variables

x^2+1.5x-10

Back to the equation:

-(x^2+1.5x-10)


We get rid of parentheses

-x^2-1.5x+10-0.5=0

We add all the numbers together, and all the variables

-1x^2-1.5x+9.5=0

a = -1; b = -1.5; c = +9.5;
Δ = b2-4ac
Δ = -1.52-4·(-1)·9.5
Δ = 40.25
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{-(-1.5)-\sqrt{40.25}}{2*-1}=\frac{1.5-\sqrt{40.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{40.25}}{2*-1}=\frac{1.5+\sqrt{40.25}}{-2}
$