Question

$3x + 9 = 2 {x}^{2}$
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Answer 1

$\Huge\mathfrak{{\orange{a}}{\blue{n}}{\pink{s}}{\purple{w}}{\red{e}}{\green{r}}:}$

$\bf{To~solve:}$

$\sf{~~~~~~3x+9=2x^{2}}$

$\sf{:→ -2x^{2}+3x+9=0}$

$\bf{It~is~a~quadratic~equation}$

$\bf\therefore{we~get:}$

$\sf{~~~~~~S=3,~~~~P=18~~~(6,~3)}$

$\sf{:→ (2x^{2}+6x)+(3x+9)=0}$

$\sf{:→ [2x(x+3)~]+[3(x+3)~]=0}$

$\sf{:→ (2x+3)(x+3)=0}$

$\sf{:→ 2x+3=0~~~~or~~~~x+3=0}$

$\sf{:→ x={\dfrac{-3}{2}}~~~or~~~x=-3}$

$\bf\therefore{The~roots~are~~{\dfrac{-3}{2}}~~and~~-3}$