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

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

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We calculate fractions


(-3x^2+4x-10)/()+(-1x^2+16x+80)/()+5=0

We multiply all the terms by the denominator


(-3x^2+4x-10)+(-1x^2+16x+80)+5*()=0

We add all the numbers together, and all the variables

(-3x^2+4x-10)+(-1x^2+16x+80)=0

We get rid of parentheses

-3x^2-1x^2+4x+16x-10+80=0

We add all the numbers together, and all the variables

-4x^2+20x+70=0

a = -4; b = 20; c = +70;
Δ = b2-4ac
Δ = 202-4·(-4)·70
Δ = 1520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{95}}{2*-4}=\frac{-20-4\sqrt{95}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{95}}{2*-4}=\frac{-20+4\sqrt{95}}{-8}
$