10x(2x+9)=-3

Solution for 10x(2x+9)=-3 equation:

10x(2x+9)=-3

We move all terms to the left:

10x(2x+9)-(-3)=0

We add all the numbers together, and all the variables

10x(2x+9)+3=0

We multiply parentheses

20x^2+90x+3=0

a = 20; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·20·3
Δ = 7860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7860}=\sqrt{4*1965}=\sqrt{4}*\sqrt{1965}=2\sqrt{1965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{1965}}{2*20}=\frac{-90-2\sqrt{1965}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{1965}}{2*20}=\frac{-90+2\sqrt{1965}}{40}
$