5x2+90x=144-9

Solution for 5x2+90x=144-9 equation:

5x^2+90x=144-9

We move all terms to the left:

5x^2+90x-(144-9)=0

We add all the numbers together, and all the variables

5x^2+90x-135=0

a = 5; b = 90; c = -135;
Δ = b2-4ac
Δ = 902-4·5·(-135)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-60\sqrt{3}}{2*5}=\frac{-90-60\sqrt{3}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+60\sqrt{3}}{2*5}=\frac{-90+60\sqrt{3}}{10}
$