5x^2+90x=144

Solution for 5x^2+90x=144 equation:

5x^2+90x=144

We move all terms to the left:

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

a = 5; b = 90; c = -144;
Δ = b2-4ac
Δ = 902-4·5·(-144)
Δ = 10980
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:

$\sqrt{\Delta}=\sqrt{10980}=\sqrt{36*305}=\sqrt{36}*\sqrt{305}=6\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{305}}{2*5}=\frac{-90-6\sqrt{305}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{305}}{2*5}=\frac{-90+6\sqrt{305}}{10}
$