8x^2+3=-x(2x-17)

Solution for 8x^2+3=-x(2x-17) equation:

8x^2+3=-x(2x-17)

We move all terms to the left:

8x^2+3-(-x(2x-17))=0


We calculate terms in parentheses: -(-x(2x-17)), so:

-x(2x-17)

We multiply parentheses

-2x^2+17x

Back to the equation:

-(-2x^2+17x)


We get rid of parentheses

8x^2+2x^2-17x+3=0

We add all the numbers together, and all the variables

10x^2-17x+3=0

a = 10; b = -17; c = +3;
Δ = b2-4ac
Δ = -172-4·10·3
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*10}=\frac{4}{20}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*10}=\frac{30}{20}
=1+1/2
$