4+5x(x-7)=13-3x

Solution for 4+5x(x-7)=13-3x equation:

4+5x(x-7)=13-3x

We move all terms to the left:

4+5x(x-7)-(13-3x)=0

We add all the numbers together, and all the variables

5x(x-7)-(-3x+13)+4=0

We multiply parentheses

5x^2-35x-(-3x+13)+4=0

We get rid of parentheses

5x^2-35x+3x-13+4=0

We add all the numbers together, and all the variables

5x^2-32x-9=0

a = 5; b = -32; c = -9;
Δ = b2-4ac
Δ = -322-4·5·(-9)
Δ = 1204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{301}}{2*5}=\frac{32-2\sqrt{301}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{301}}{2*5}=\frac{32+2\sqrt{301}}{10}
$