345x+5x^2=8100

Solution for 345x+5x^2=8100 equation:

345x+5x^2=8100

We move all terms to the left:

345x+5x^2-(8100)=0

a = 5; b = 345; c = -8100;
Δ = b2-4ac
Δ = 3452-4·5·(-8100)
Δ = 281025
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:

$\sqrt{\Delta}=\sqrt{281025}=\sqrt{225*1249}=\sqrt{225}*\sqrt{1249}=15\sqrt{1249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(345)-15\sqrt{1249}}{2*5}=\frac{-345-15\sqrt{1249}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(345)+15\sqrt{1249}}{2*5}=\frac{-345+15\sqrt{1249}}{10}
$