10x+4=15x^2+5x

Solution for 10x+4=15x^2+5x equation:

10x+4=15x^2+5x

We move all terms to the left:

10x+4-(15x^2+5x)=0

We get rid of parentheses

-15x^2+10x-5x+4=0

We add all the numbers together, and all the variables

-15x^2+5x+4=0

a = -15; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-15)·4
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{265}}{2*-15}=\frac{-5-\sqrt{265}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{265}}{2*-15}=\frac{-5+\sqrt{265}}{-30}
$