4(15.75x+8)=2x^2

Solution for 4(15.75x+8)=2x^2 equation:

4(15.75x+8)=2x^2

We move all terms to the left:

4(15.75x+8)-(2x^2)=0

determiningTheFunctionDomain
-2x^2+4(15.75x+8)=0

We multiply parentheses

-2x^2+60x+32=0

a = -2; b = 60; c = +32;
Δ = b2-4ac
Δ = 602-4·(-2)·32
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{241}}{2*-2}=\frac{-60-4\sqrt{241}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{241}}{2*-2}=\frac{-60+4\sqrt{241}}{-4}
$