Solve (1,4+x)(1,4-x)=(x-1,7)(7,6-x)

$$( 1,4 + x ) ( 1,4 - x ) = ( x - 1,7 ) ( 7,6 - x )$$

Solve for x

$$x=1,6$$

Steps for Solving Linear Equation

Consider \left(1,4+x\right)\left(1,4-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1,4.

$$1,96-x^{2}=\left(x-1,7\right)\left(7,6-x\right)$$

Use the distributive property to multiply x-1,7 by 7,6-x and combine like terms.

$$1,96-x^{2}=9,3x-x^{2}-12,92$$

Subtract 9,3x from both sides.

$$1,96-x^{2}-9,3x=-x^{2}-12,92$$

Add x^{2} to both sides.

$$1,96-x^{2}-9,3x+x^{2}=-12,92$$

Combine -x^{2} and x^{2} to get 0.

$$1,96-9,3x=-12,92$$

Subtract 1,96 from both sides.

$$-9,3x=-12,92-1,96$$

Subtract 1,96 from -12,92 to get -14,88.

$$-9,3x=-14,88$$

Divide both sides by -9,3.

$$x=\frac{-14,88}{-9,3}$$

Expand \frac{-14,88}{-9,3} by multiplying both numerator and the denominator by 100.

$$x=\frac{-1488}{-930}$$

Reduce the fraction \frac{-1488}{-930} to lowest terms by extracting and canceling out -186.

$$x=\frac{8}{5}$$