0.5(x+7)(x-2)=26

Solution for 0.5(x+7)(x-2)=26 equation:

0.5(x+7)(x-2)=26

We move all terms to the left:

0.5(x+7)(x-2)-(26)=0

We multiply parentheses ..

0.5(+x^2-2x+7x-14)-26=0

We multiply parentheses

0.5x^2-1x+3.5x-7-26=0

We add all the numbers together, and all the variables

0.5x^2+2.5x-33=0

a = 0.5; b = 2.5; c = -33;
Δ = b2-4ac
Δ = 2.52-4·0.5·(-33)
Δ = 72.25
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{-(2.5)-\sqrt{72.25}}{2*0.5}=\frac{-2.5-\sqrt{72.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{72.25}}{2*0.5}=\frac{-2.5+\sqrt{72.25}}{1}
$