215x+200=5x^2

Solution for 215x+200=5x^2 equation:

215x+200=5x^2

We move all terms to the left:

215x+200-(5x^2)=0

determiningTheFunctionDomain
-5x^2+215x+200=0

a = -5; b = 215; c = +200;
Δ = b2-4ac
Δ = 2152-4·(-5)·200
Δ = 50225
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:

$\sqrt{\Delta}=\sqrt{50225}=\sqrt{1225*41}=\sqrt{1225}*\sqrt{41}=35\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(215)-35\sqrt{41}}{2*-5}=\frac{-215-35\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(215)+35\sqrt{41}}{2*-5}=\frac{-215+35\sqrt{41}}{-10}
$