x=3/4x+7=-7

Solution for x=3/4x+7=-7 equation:

x=3/4x+7=-7

We move all terms to the left:

x-(3/4x+7)=0


Domain of the equation: 4x+7)!=0

x∈R


We get rid of parentheses

x-3/4x-7=0

We multiply all the terms by the denominator


x*4x-7*4x-3=0

Wy multiply elements

4x^2-28x-3=0

a = 4; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·4·(-3)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{13}}{2*4}=\frac{28-8\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{13}}{2*4}=\frac{28+8\sqrt{13}}{8}
$