0.5x^2-2x-7=3x-15

Solution for 0.5x^2-2x-7=3x-15 equation:

0.5x^2-2x-7=3x-15

We move all terms to the left:

0.5x^2-2x-7-(3x-15)=0

We get rid of parentheses

0.5x^2-2x-3x+15-7=0

We add all the numbers together, and all the variables

0.5x^2-5x+8=0

a = 0.5; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·0.5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*0.5}=\frac{2}{1}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*0.5}=\frac{8}{1}
=8
$