4x(5x+2)=9

Solution for 4x(5x+2)=9 equation:

4x(5x+2)=9

We move all terms to the left:

4x(5x+2)-(9)=0

We multiply parentheses

20x^2+8x-9=0

a = 20; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·20·(-9)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*20}=\frac{-36}{40}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*20}=\frac{20}{40}
=1/2
$