2x^2+3x=900

Solution for 2x^2+3x=900 equation:

2x^2+3x=900

We move all terms to the left:

2x^2+3x-(900)=0

a = 2; b = 3; c = -900;
Δ = b2-4ac
Δ = 32-4·2·(-900)
Δ = 7209
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:

$\sqrt{\Delta}=\sqrt{7209}=\sqrt{81*89}=\sqrt{81}*\sqrt{89}=9\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9\sqrt{89}}{2*2}=\frac{-3-9\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9\sqrt{89}}{2*2}=\frac{-3+9\sqrt{89}}{4}
$