4(7+5x2)=78

Solution for 4(7+5x2)=78 equation:

4(7+5x^2)=78

We move all terms to the left:

4(7+5x^2)-(78)=0

We multiply parentheses

20x^2+28-78=0

We add all the numbers together, and all the variables

20x^2-50=0

a = 20; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·20·(-50)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*20}=\frac{0-20\sqrt{10}}{40}
=-\frac{20\sqrt{10}}{40}
=-\frac{\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*20}=\frac{0+20\sqrt{10}}{40}
=\frac{20\sqrt{10}}{40}
=\frac{\sqrt{10}}{2}
$