X-7=-3(x+3)/5

Solution for X-7=-3(x+3)/5 equation:

X-7=-3(X+3)/5

We move all terms to the left:

X-7-(-3(X+3)/5)=0

We multiply all the terms by the denominator


X*5)-(-3(X+3)-7*5)=0

We add all the numbers together, and all the variables

X*5)-(-3(X+3)=0

We multiply parentheses

X*5)-(-3X-9=0

Wy multiply elements

5X^2-3X-9=0

a = 5; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·5·(-9)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*5}=\frac{3-3\sqrt{21}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*5}=\frac{3+3\sqrt{21}}{10}
$