-2^x=3/4x+5

Solution for -2^x=3/4x+5 equation:

-2^x=3/4x+5

We move all terms to the left:

-2^x-(3/4x+5)=0


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

-2^x-3/4x-5=0

We multiply all the terms by the denominator


-2^x*4x-5*4x-3=0

Wy multiply elements

-8x^2-20x-3=0

a = -8; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·(-8)·(-3)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{19}}{2*-8}=\frac{20-4\sqrt{19}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{19}}{2*-8}=\frac{20+4\sqrt{19}}{-16}
$