(2x-7/2)(x+2)-(x+4)(x-7/2)+5=0

Solution for (2x-7/2)(x+2)-(x+4)(x-7/2)+5=0 equation:

(2x-7/2)(x+2)-(x+4)(x-7/2)+5=0


Domain of the equation: 2)(x+2)!=0

x∈R


We add all the numbers together, and all the variables

(+2x-7/2)(x+2)-(x+4)(+x-7/2)+5=0

We multiply parentheses ..

(+2x^2+4x-7x^2-7/2*2)-(x+4)(+x-7/2)+5=0

We calculate fractions


(-5x^2+4x-14)/()+(-1x^2+24x+112)/()+5=0

We multiply all the terms by the denominator


(-5x^2+4x-14)+(-1x^2+24x+112)+5*()=0

We add all the numbers together, and all the variables

(-5x^2+4x-14)+(-1x^2+24x+112)=0

We get rid of parentheses

-5x^2-1x^2+4x+24x-14+112=0

We add all the numbers together, and all the variables

-6x^2+28x+98=0

a = -6; b = 28; c = +98;
Δ = b2-4ac
Δ = 282-4·(-6)·98
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-56}{2*-6}=\frac{-84}{-12}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+56}{2*-6}=\frac{28}{-12}
=-2+1/3
$