5x^2+19x=150=180

Solution for 5x^2+19x=150=180 equation:

5x^2+19x=150=180

We move all terms to the left:

5x^2+19x-(150)=0

a = 5; b = 19; c = -150;
Δ = b2-4ac
Δ = 192-4·5·(-150)
Δ = 3361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{3361}}{2*5}=\frac{-19-\sqrt{3361}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{3361}}{2*5}=\frac{-19+\sqrt{3361}}{10}
$