45x+2x^2=1025

Solution for 45x+2x^2=1025 equation:

45x+2x^2=1025

We move all terms to the left:

45x+2x^2-(1025)=0

a = 2; b = 45; c = -1025;
Δ = b2-4ac
Δ = 452-4·2·(-1025)
Δ = 10225
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:

$\sqrt{\Delta}=\sqrt{10225}=\sqrt{25*409}=\sqrt{25}*\sqrt{409}=5\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{409}}{2*2}=\frac{-45-5\sqrt{409}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{409}}{2*2}=\frac{-45+5\sqrt{409}}{4}
$