0.5(x-12)+2=1.25x(x+8)-9.5

Solution for 0.5(x-12)+2=1.25x(x+8)-9.5 equation:

0.5(x-12)+2=1.25x(x+8)-9.5

We move all terms to the left:

0.5(x-12)+2-(1.25x(x+8)-9.5)=0

We multiply parentheses

0.5x-(1.25x(x+8)-9.5)-6+2=0


We calculate terms in parentheses: -(1.25x(x+8)-9.5), so:

1.25x(x+8)-9.5

We multiply parentheses

x^2+8x-9.5

Back to the equation:

-(x^2+8x-9.5)


We add all the numbers together, and all the variables

0.5x-(x^2+8x-9.5)-4=0

We get rid of parentheses

-x^2+0.5x-8x+9.5-4=0

We add all the numbers together, and all the variables

-1x^2-7.5x+5.5=0

a = -1; b = -7.5; c = +5.5;
Δ = b2-4ac
Δ = -7.52-4·(-1)·5.5
Δ = 78.25
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{-(-7.5)-\sqrt{78.25}}{2*-1}=\frac{7.5-\sqrt{78.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{78.25}}{2*-1}=\frac{7.5+\sqrt{78.25}}{-2}
$