4x^2+2x=7x+21

Solution for 4x^2+2x=7x+21 equation:

4x^2+2x=7x+21

We move all terms to the left:

4x^2+2x-(7x+21)=0

We get rid of parentheses

4x^2+2x-7x-21=0

We add all the numbers together, and all the variables

4x^2-5x-21=0

a = 4; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·4·(-21)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*4}=\frac{-14}{8}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*4}=\frac{24}{8}
=3
$