(3x+7)(9x-43)=90

Solution for (3x+7)(9x-43)=90 equation:

(3x+7)(9x-43)=90

We move all terms to the left:

(3x+7)(9x-43)-(90)=0

We multiply parentheses ..

(+27x^2-129x+63x-301)-90=0

We get rid of parentheses

27x^2-129x+63x-301-90=0

We add all the numbers together, and all the variables

27x^2-66x-391=0

a = 27; b = -66; c = -391;
Δ = b2-4ac
Δ = -662-4·27·(-391)
Δ = 46584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{46584}=\sqrt{36*1294}=\sqrt{36}*\sqrt{1294}=6\sqrt{1294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{1294}}{2*27}=\frac{66-6\sqrt{1294}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{1294}}{2*27}=\frac{66+6\sqrt{1294}}{54}
$