x=-0.5(x-10)(x+14)

Solution for x=-0.5(x-10)(x+14) equation:

x=-0.5(x-10)(x+14)

We move all terms to the left:

x-(-0.5(x-10)(x+14))=0

We multiply parentheses ..

-(-0.5(+x^2+14x-10x-140))+x=0


We calculate terms in parentheses: -(-0.5(+x^2+14x-10x-140)), so:

-0.5(+x^2+14x-10x-140)

We multiply parentheses

-0.5x^2-7x+5x+70

We add all the numbers together, and all the variables

-0.5x^2-2x+70

Back to the equation:

-(-0.5x^2-2x+70)


We get rid of parentheses

0.5x^2+2x+x-70=0

We add all the numbers together, and all the variables

0.5x^2+3x-70=0

a = 0.5; b = 3; c = -70;
Δ = b2-4ac
Δ = 32-4·0.5·(-70)
Δ = 149
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{149}}{2*0.5}=\frac{-3-\sqrt{149}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*0.5}=\frac{-3+\sqrt{149}}{1}
$