(7x+4)-(x-9)x=2.5

Solution for (7x+4)-(x-9)x=2.5 equation:

(7x+4)-(x-9)x=2.5

We move all terms to the left:

(7x+4)-(x-9)x-(2.5)=0

We add all the numbers together, and all the variables

(7x+4)-(x-9)x-2.5=0

We multiply parentheses

-x^2+(7x+4)+9x-2.5=0

We get rid of parentheses

-x^2+7x+9x+4-2.5=0

We add all the numbers together, and all the variables

-1x^2+16x+1.5=0

a = -1; b = 16; c = +1.5;
Δ = b2-4ac
Δ = 162-4·(-1)·1.5
Δ = 262
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{-(16)-\sqrt{262}}{2*-1}=\frac{-16-\sqrt{262}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+\sqrt{262}}{2*-1}=\frac{-16+\sqrt{262}}{-2}
$