26=2x^2+3x

Solution for 26=2x^2+3x equation:

26=2x^2+3x

We move all terms to the left:

26-(2x^2+3x)=0

We get rid of parentheses

-2x^2-3x+26=0

a = -2; b = -3; c = +26;
Δ = b2-4ac
Δ = -32-4·(-2)·26
Δ = 217
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{-(-3)-\sqrt{217}}{2*-2}=\frac{3-\sqrt{217}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{217}}{2*-2}=\frac{3+\sqrt{217}}{-4}
$