(2x+9)7x=90

Solution for (2x+9)7x=90 equation:

(2x+9)7x=90

We move all terms to the left:

(2x+9)7x-(90)=0

We multiply parentheses

14x^2+63x-90=0

a = 14; b = 63; c = -90;
Δ = b2-4ac
Δ = 632-4·14·(-90)
Δ = 9009
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:

$\sqrt{\Delta}=\sqrt{9009}=\sqrt{9*1001}=\sqrt{9}*\sqrt{1001}=3\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{1001}}{2*14}=\frac{-63-3\sqrt{1001}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{1001}}{2*14}=\frac{-63+3\sqrt{1001}}{28}
$