15(6x2+7)=38(24x+3)

Solution for 15(6x2+7)=38(24x+3) equation:

15(6x^2+7)=38(24x+3)

We move all terms to the left:

15(6x^2+7)-(38(24x+3))=0

We multiply parentheses

90x^2-(38(24x+3))+105=0


We calculate terms in parentheses: -(38(24x+3)), so:

38(24x+3)

We multiply parentheses

912x+114

Back to the equation:

-(912x+114)


We get rid of parentheses

90x^2-912x-114+105=0

We add all the numbers together, and all the variables

90x^2-912x-9=0

a = 90; b = -912; c = -9;
Δ = b2-4ac
Δ = -9122-4·90·(-9)
Δ = 834984
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:

$\sqrt{\Delta}=\sqrt{834984}=\sqrt{36*23194}=\sqrt{36}*\sqrt{23194}=6\sqrt{23194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-912)-6\sqrt{23194}}{2*90}=\frac{912-6\sqrt{23194}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-912)+6\sqrt{23194}}{2*90}=\frac{912+6\sqrt{23194}}{180}
$