x=-3.5(x+4)3x-0.5

Solution for x=-3.5(x+4)3x-0.5 equation:

x=-3.5(x+4)3x-0.5

We move all terms to the left:

x-(-3.5(x+4)3x-0.5)=0


We calculate terms in parentheses: -(-3.5(x+4)3x-0.5), so:

-3.5(x+4)3x-0.5

We multiply parentheses

-10x^2-40x-0.5

Back to the equation:

-(-10x^2-40x-0.5)


We get rid of parentheses

10x^2+40x+x+0.5=0

We add all the numbers together, and all the variables

10x^2+41x+0.5=0

a = 10; b = 41; c = +0.5;
Δ = b2-4ac
Δ = 412-4·10·0.5
Δ = 1661
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{-(41)-\sqrt{1661}}{2*10}=\frac{-41-\sqrt{1661}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1661}}{2*10}=\frac{-41+\sqrt{1661}}{20}
$