(5x+7)(9x+1)=2688

Solution for (5x+7)(9x+1)=2688 equation:

(5x+7)(9x+1)=2688

We move all terms to the left:

(5x+7)(9x+1)-(2688)=0

We multiply parentheses ..

(+45x^2+5x+63x+7)-2688=0

We get rid of parentheses

45x^2+5x+63x+7-2688=0

We add all the numbers together, and all the variables

45x^2+68x-2681=0

a = 45; b = 68; c = -2681;
Δ = b2-4ac
Δ = 682-4·45·(-2681)
Δ = 487204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{487204}=698$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-698}{2*45}=\frac{-766}{90}
=-8+23/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+698}{2*45}=\frac{630}{90}
=7
$