2x(x+1)=7x+3

Solution for 2x(x+1)=7x+3 equation:

2x(x+1)=7x+3

We move all terms to the left:

2x(x+1)-(7x+3)=0

We multiply parentheses

2x^2+2x-(7x+3)=0

We get rid of parentheses

2x^2+2x-7x-3=0

We add all the numbers together, and all the variables

2x^2-5x-3=0

a = 2; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*2}=\frac{12}{4}
=3
$