Given, equation is √3x2+x+5=x−3 Here, 3x2+x+5≥0 (since square root is non-negative) ‌⇒‌‌x−3≥0 ‌⇒‌‌x≥3 Now, squaring to both sides of given equation, we get ‌(√3x2+x+5)2=(x−3)2 ⇒3x2+x+5=x2−6x+9 ⇒2x2+7x−4=0 Using quadratic formula, x‌=‌
−7±√72−4⋅2⋅(−4)
2â‹…2
‌=‌
−7±√49+32
4
=‌
−7±9
4
⇒‌‌x‌=‌
2
4
‌ and ‌x=‌
−16
4
⇒‌‌x‌=‌
1
2
‌ and ‌x=−4 Since domain, x≥3, so x=−4 And x=‌
