7x-2=x(x+1)+5x-4

Solution for 7x-2=x(x+1)+5x-4 equation:

7x-2=x(x+1)+5x-4

We move all terms to the left:

7x-2-(x(x+1)+5x-4)=0


We calculate terms in parentheses: -(x(x+1)+5x-4), so:

x(x+1)+5x-4

We add all the numbers together, and all the variables

5x+x(x+1)-4

We multiply parentheses

x^2+5x+x-4

We add all the numbers together, and all the variables

x^2+6x-4

Back to the equation:

-(x^2+6x-4)


We get rid of parentheses

-x^2+7x-6x+4-2=0

We add all the numbers together, and all the variables

-1x^2+x+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$