2x2=25x+42

Solution for 2x2=25x+42 equation:

2x^2=25x+42

We move all terms to the left:

2x^2-(25x+42)=0

We get rid of parentheses

2x^2-25x-42=0

a = 2; b = -25; c = -42;
Δ = b2-4ac
Δ = -252-4·2·(-42)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-31}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+31}{2*2}=\frac{56}{4}
=14
$