5x2+3x=54

Solution for 5x2+3x=54 equation:

5x^2+3x=54

We move all terms to the left:

5x^2+3x-(54)=0

a = 5; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·5·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-33}{2*5}=\frac{-36}{10}
=-3+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*5}=\frac{30}{10}
=3
$