4(-1/2x+7)5x=15

Solution for 4(-1/2x+7)5x=15 equation:

4(-1/2x+7)5x=15

We move all terms to the left:

4(-1/2x+7)5x-(15)=0


Domain of the equation: 2x+7)5x!=0

x∈R


We multiply parentheses

-20x^2+140x-15=0

a = -20; b = 140; c = -15;
Δ = b2-4ac
Δ = 1402-4·(-20)·(-15)
Δ = 18400
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:

$\sqrt{\Delta}=\sqrt{18400}=\sqrt{400*46}=\sqrt{400}*\sqrt{46}=20\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{46}}{2*-20}=\frac{-140-20\sqrt{46}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{46}}{2*-20}=\frac{-140+20\sqrt{46}}{-40}
$