x=4,x2+7x

Solution for x=4,x2+7x equation:

x=4.x^2+7x

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2-6x=0

a = -4; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-4)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-4}=\frac{12}{-8}
=-1+1/2
$