(5x+6)(9x+7)=0

Solution for (5x+6)(9x+7)=0 equation:

(5x+6)(9x+7)=0

We multiply parentheses ..

(+45x^2+35x+54x+42)=0

We get rid of parentheses

45x^2+35x+54x+42=0

We add all the numbers together, and all the variables

45x^2+89x+42=0

a = 45; b = 89; c = +42;
Δ = b2-4ac
Δ = 892-4·45·42
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-19}{2*45}=\frac{-108}{90}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+19}{2*45}=\frac{-70}{90}
=-7/9
$