(5x-7)(9x+2)=0

Solution for (5x-7)(9x+2)=0 equation:

(5x-7)(9x+2)=0

We multiply parentheses ..

(+45x^2+10x-63x-14)=0

We get rid of parentheses

45x^2+10x-63x-14=0

We add all the numbers together, and all the variables

45x^2-53x-14=0

a = 45; b = -53; c = -14;
Δ = b2-4ac
Δ = -532-4·45·(-14)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-73}{2*45}=\frac{-20}{90}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+73}{2*45}=\frac{126}{90}
=1+2/5
$