2x(x+1)=7x+8

Solution for 2x(x+1)=7x+8 equation:

2x(x+1)=7x+8

We move all terms to the left:

2x(x+1)-(7x+8)=0

We multiply parentheses

2x^2+2x-(7x+8)=0

We get rid of parentheses

2x^2+2x-7x-8=0

We add all the numbers together, and all the variables

2x^2-5x-8=0

a = 2; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·2·(-8)
Δ = 89
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{-(-5)-\sqrt{89}}{2*2}=\frac{5-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{89}}{2*2}=\frac{5+\sqrt{89}}{4}
$