Question

5(3x+1)^2+6(3x+1)-8=0​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

=> 5(3x+1)²+6(3x+1)-8=0

Now, expanding the terms and opening the brackets

=> 5( 3x+1)²+6*3x+6*1-8=0

Identity: (a+b)²= a²+b²+2ab

=> 5[ (3x)²+1²+2(3x)(1)] +18x +6-8=0

=> 5( 9x²+1+6x) +18x-2=0

=> 45x²+5+30x+18x-2=0

=> 45x²+48x+5-2=0

=> 45x²+48x +3=0

Now, it is in the form of a quadratic equation

so, factorise it

By using quadratic formula

a= 45,b= 48 & c= 3

x= -b±√b²-4ac /2a

x= -48±√ 48²-4(45)(3)/2(45)

x= -48±√ 2304-540/90

x= -48±√ 1764/90

Here, the discriminant b²-4ac >0 so ,there will be two real roots

x= -48±42/90

x= -6/90 or x = -90/90

x= -1/15 or x = -1

Answer 2

$\huge\color{cyan}\boxed{\colorbox{black}{answer:}}$

=> 5(3x+1)²+6(3x+1)-8=0

Now, expanding the terms and opening the brackets

=> 5( 3x+1)²+6*3x+6*1-8=0

Identity: (a+b)²= a²+b²+2ab

=> 5[ (3x)²+1²+2(3x)(1)] +18x +6-8=0

=> 5( 9x²+1+6x) +18x-2=0

=> 45x²+5+30x+18x-2=0

=> 45x²+48x+5-2=0

=> 45x²+48x +3=0

Now, it is in the form of a quadratic equation

so, factorise it

By using quadratic formula

a= 45,b= 48 & c= 3

x= -b±√b²-4ac /2a

x= -48±√ 48²-4(45)(3)/2(45)

x= -48±√ 2304-540/90

x= -48±√ 1764/90

Here, the discriminant b²-4ac >0 so ,there will be two real roots

x= -48±42/90

x= -6/90 or x = -90/90

x= -1/15 or x = -1