Solve for x
x=10
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\left(\sqrt{4x-15}\right)^{2}=\left(\frac{6x-20}{\sqrt{9x-26}}\right)^{2}
Square both sides of the equation.
4x-15=\left(\frac{6x-20}{\sqrt{9x-26}}\right)^{2}
Calculate \sqrt{4x-15} to the power of 2 and get 4x-15.
4x-15=\frac{\left(6x-20\right)^{2}}{\left(\sqrt{9x-26}\right)^{2}}
To raise \frac{6x-20}{\sqrt{9x-26}} to a power, raise both numerator and denominator to the power and then divide.
4x-15=\frac{36x^{2}-240x+400}{\left(\sqrt{9x-26}\right)^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-20\right)^{2}.
4x-15=\frac{36x^{2}-240x+400}{9x-26}
Calculate \sqrt{9x-26} to the power of 2 and get 9x-26.
4x\left(9x-26\right)+\left(9x-26\right)\left(-15\right)=36x^{2}-240x+400
Multiply both sides of the equation by 9x-26.
36x^{2}-104x+\left(9x-26\right)\left(-15\right)=36x^{2}-240x+400
Use the distributive property to multiply 4x by 9x-26.
36x^{2}-104x-135x+390=36x^{2}-240x+400
Use the distributive property to multiply 9x-26 by -15.
36x^{2}-239x+390=36x^{2}-240x+400
Combine -104x and -135x to get -239x.
36x^{2}-239x+390-36x^{2}=-240x+400
Subtract 36x^{2} from both sides.
-239x+390=-240x+400
Combine 36x^{2} and -36x^{2} to get 0.
-239x+390+240x=400
Add 240x to both sides.
x+390=400
Combine -239x and 240x to get x.
x=400-390
Subtract 390 from both sides.
x=10
Subtract 390 from 400 to get 10.
\sqrt{4\times 10-15}=\frac{6\times 10-20}{\sqrt{9\times 10-26}}
Substitute 10 for x in the equation \sqrt{4x-15}=\frac{6x-20}{\sqrt{9x-26}}.
5=5
Simplify. The value x=10 satisfies the equation.
x=10
Equation \sqrt{4x-15}=\frac{6x-20}{\sqrt{9x-26}} has a unique solution.
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