5x^2-23x=-18

Solution for 5x^2-23x=-18 equation:

5x^2-23x=-18

We move all terms to the left:

5x^2-23x-(-18)=0

We add all the numbers together, and all the variables

5x^2-23x+18=0

a = 5; b = -23; c = +18;
Δ = b2-4ac
Δ = -232-4·5·18
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*5}=\frac{36}{10}
=3+3/5
$