2x2=23x+39

Solution for 2x2=23x+39 equation:

2x^2=23x+39

We move all terms to the left:

2x^2-(23x+39)=0

We get rid of parentheses

2x^2-23x-39=0

a = 2; b = -23; c = -39;
Δ = b2-4ac
Δ = -232-4·2·(-39)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-29}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+29}{2*2}=\frac{52}{4}
=13
$