(9x+1)(5x+6)=0

Solution for (9x+1)(5x+6)=0 equation:

(9x+1)(5x+6)=0

We multiply parentheses ..

(+45x^2+54x+5x+6)=0

We get rid of parentheses

45x^2+54x+5x+6=0

We add all the numbers together, and all the variables

45x^2+59x+6=0

a = 45; b = 59; c = +6;
Δ = b2-4ac
Δ = 592-4·45·6
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-49}{2*45}=\frac{-108}{90}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+49}{2*45}=\frac{-10}{90}
=-1/9
$