(4x-9)7x=90

Solution for (4x-9)7x=90 equation:

(4x-9)7x=90

We move all terms to the left:

(4x-9)7x-(90)=0

We multiply parentheses

28x^2-63x-90=0

a = 28; b = -63; c = -90;
Δ = b2-4ac
Δ = -632-4·28·(-90)
Δ = 14049
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:

$\sqrt{\Delta}=\sqrt{14049}=\sqrt{9*1561}=\sqrt{9}*\sqrt{1561}=3\sqrt{1561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{1561}}{2*28}=\frac{63-3\sqrt{1561}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{1561}}{2*28}=\frac{63+3\sqrt{1561}}{56}
$