5(x-7)x=4

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

5(x-7)x=4

We move all terms to the left:

5(x-7)x-(4)=0

We multiply parentheses

5x^2-35x-4=0

a = 5; b = -35; c = -4;
Δ = b2-4ac
Δ = -352-4·5·(-4)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{145}}{2*5}=\frac{35-3\sqrt{145}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{145}}{2*5}=\frac{35+3\sqrt{145}}{10}
$