114=(2x-3)(x)

Solution for 114=(2x-3)(x) equation:

114=(2x-3)(x)

We move all terms to the left:

114-((2x-3)(x))=0


We calculate terms in parentheses: -((2x-3)x), so:

(2x-3)x

We multiply parentheses

2x^2-3x

Back to the equation:

-(2x^2-3x)


We get rid of parentheses

-2x^2+3x+114=0

a = -2; b = 3; c = +114;
Δ = b2-4ac
Δ = 32-4·(-2)·114
Δ = 921
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{921}}{2*-2}=\frac{-3-\sqrt{921}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{921}}{2*-2}=\frac{-3+\sqrt{921}}{-4}
$