2x^2-15x=-23

Solution for 2x^2-15x=-23 equation:

2x^2-15x=-23

We move all terms to the left:

2x^2-15x-(-23)=0

We add all the numbers together, and all the variables

2x^2-15x+23=0

a = 2; b = -15; c = +23;
Δ = b2-4ac
Δ = -152-4·2·23
Δ = 41
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{-(-15)-\sqrt{41}}{2*2}=\frac{15-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{41}}{2*2}=\frac{15+\sqrt{41}}{4}
$