9x*30x+4=9x*20x+8

Solution for 9x*30x+4=9x*20x+8 equation:

9x*30x+4=9x*20x+8

We move all terms to the left:

9x*30x+4-(9x*20x+8)=0

Wy multiply elements

270x^2-(9x*20x+8)+4=0

We get rid of parentheses

270x^2-9x*20x-8+4=0

We add all the numbers together, and all the variables

270x^2-9x*20x-4=0

Wy multiply elements

270x^2-180x^2-4=0

We add all the numbers together, and all the variables

90x^2-4=0

a = 90; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·90·(-4)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*90}=\frac{0-12\sqrt{10}}{180}
=-\frac{12\sqrt{10}}{180}
=-\frac{\sqrt{10}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*90}=\frac{0+12\sqrt{10}}{180}
=\frac{12\sqrt{10}}{180}
=\frac{\sqrt{10}}{15}
$