9x-43=-2x(x+5)

Solution for 9x-43=-2x(x+5) equation:

9x-43=-2x(x+5)

We move all terms to the left:

9x-43-(-2x(x+5))=0


We calculate terms in parentheses: -(-2x(x+5)), so:

-2x(x+5)

We multiply parentheses

-2x^2-10x

Back to the equation:

-(-2x^2-10x)


We get rid of parentheses

2x^2+10x+9x-43=0

We add all the numbers together, and all the variables

2x^2+19x-43=0

a = 2; b = 19; c = -43;
Δ = b2-4ac
Δ = 192-4·2·(-43)
Δ = 705
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{-(19)-\sqrt{705}}{2*2}=\frac{-19-\sqrt{705}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{705}}{2*2}=\frac{-19+\sqrt{705}}{4}
$