Solve by isolating the root signs and squaring both sides

Question

7+ √3x = √5x+4 +5

Answer 1

7+√3x=√(5x+4)+5

7-5=√(5x+4)-√3x

2=√(5x+4)-√3x

square both sides

4=(5x+4)-2√(3x(5x+4))+3x

4=8x+4-2√(15x²+12x)

4-4=8x-2√(15x²+12x)

0=8x-2√(15x²+12x)

-8x=-2√(15x²+12x)

divide both sides by -2

4x=√(15x²+12x)

square both sides

16x²=15x²+12x

16x²-15x²-12x=0

x²-12x=0

factor

x(x-12)=0

x=0

x-12=0

x=12

there are two solutions: x=0 and x=12

Answer 2

7+√3x=√5x+4+5
Simplifies to:
1.732051x+7=2.236068x+9
Let's solve your equation step-by-step.
1.732051x+7=2.236068x+9
Step 1: Subtract 2.236068x from both sides.
1.732051x+7−2.236068x=2.236068x+9−2.236068x
−0.504017x+7=9
Step 2: Subtract 7 from both sides.
−0.504017x+7−7=9−7
−0.504017x=2
Step 3: Divide both sides by -0.504017.
−0.504017x
−0.504017
=
2
−0.504017
x=−3.96812
Answer:
x=−3.96812