4(-1/2x+7)x=15

Solution for 4(-1/2x+7)x=15 equation:

4(-1/2x+7)x=15

We move all terms to the left:

4(-1/2x+7)x-(15)=0


Domain of the equation: 2x+7)x!=0

x∈R


We multiply parentheses

-4x^2+28x-15=0

a = -4; b = 28; c = -15;
Δ = b2-4ac
Δ = 282-4·(-4)·(-15)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{34}}{2*-4}=\frac{-28-4\sqrt{34}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{34}}{2*-4}=\frac{-28+4\sqrt{34}}{-8}
$