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8x^{2}-60=-7x^{2}
Subtract 60 from both sides.
8x^{2}-60+7x^{2}=0
Add 7x^{2} to both sides.
15x^{2}-60=0
Combine 8x^{2} and 7x^{2} to get 15x^{2}.
x^{2}-4=0
Divide both sides by 15.
\left(x-2\right)\left(x+2\right)=0
Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=2 x=-2
To find equation solutions, solve x-2=0 and x+2=0.
8x^{2}+7x^{2}=60
Add 7x^{2} to both sides.
15x^{2}=60
Combine 8x^{2} and 7x^{2} to get 15x^{2}.
x^{2}=\frac{60}{15}
Divide both sides by 15.
x^{2}=4
Divide 60 by 15 to get 4.
x=2 x=-2
Take the square root of both sides of the equation.
8x^{2}-60=-7x^{2}
Subtract 60 from both sides.
8x^{2}-60+7x^{2}=0
Add 7x^{2} to both sides.
15x^{2}-60=0
Combine 8x^{2} and 7x^{2} to get 15x^{2}.
x=\frac{0±\sqrt{0^{2}-4\times 15\left(-60\right)}}{2\times 15}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 15\left(-60\right)}}{2\times 15}
Square 0.
x=\frac{0±\sqrt{-60\left(-60\right)}}{2\times 15}
Multiply -4 times 15.
x=\frac{0±\sqrt{3600}}{2\times 15}
Multiply -60 times -60.
x=\frac{0±60}{2\times 15}
Take the square root of 3600.
x=\frac{0±60}{30}
Multiply 2 times 15.
x=2
Now solve the equation x=\frac{0±60}{30} when ± is plus. Divide 60 by 30.
x=-2
Now solve the equation x=\frac{0±60}{30} when ± is minus. Divide -60 by 30.
x=2 x=-2
The equation is now solved.