5x^2+2x+3=150

Solution for 5x^2+2x+3=150 equation:

5x^2+2x+3=150

We move all terms to the left:

5x^2+2x+3-(150)=0

We add all the numbers together, and all the variables

5x^2+2x-147=0

a = 5; b = 2; c = -147;
Δ = b2-4ac
Δ = 22-4·5·(-147)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{46}}{2*5}=\frac{-2-8\sqrt{46}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{46}}{2*5}=\frac{-2+8\sqrt{46}}{10}
$