3(5x2)=4(3x+6)

Solution for 3(5x2)=4(3x+6) equation:

3(5x^2)=4(3x+6)

We move all terms to the left:

3(5x^2)-(4(3x+6))=0


We calculate terms in parentheses: -(4(3x+6)), so:

4(3x+6)

We multiply parentheses

12x+24

Back to the equation:

-(12x+24)


We get rid of parentheses

35x^2-12x-24=0

a = 35; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·35·(-24)
Δ = 3504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{219}}{2*35}=\frac{12-4\sqrt{219}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{219}}{2*35}=\frac{12+4\sqrt{219}}{70}
$