8x+10=3x^2=15x

Solution for 8x+10=3x^2=15x equation:

8x+10=3x^2=15x

We move all terms to the left:

8x+10-(3x^2)=0

determiningTheFunctionDomain
-3x^2+8x+10=0

a = -3; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-3)·10
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*-3}=\frac{-8-2\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*-3}=\frac{-8+2\sqrt{46}}{-6}
$