(2x-1)=2x^2+5x-12=

Solution for (2x-1)=2x^2+5x-12= equation:

(2x-1)=2x^2+5x-12=

We move all terms to the left:

(2x-1)-(2x^2+5x-12)=0

We get rid of parentheses

-2x^2+2x-5x-1+12=0

We add all the numbers together, and all the variables

-2x^2-3x+11=0

a = -2; b = -3; c = +11;
Δ = b2-4ac
Δ = -32-4·(-2)·11
Δ = 97
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{97}}{2*-2}=\frac{3-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{97}}{2*-2}=\frac{3+\sqrt{97}}{-4}
$