7x=4-15x^2

Solution for 7x=4-15x^2 equation:

7x=4-15x^2

We move all terms to the left:

7x-(4-15x^2)=0

We get rid of parentheses

15x^2+7x-4=0

a = 15; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·15·(-4)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*15}=\frac{-24}{30}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*15}=\frac{10}{30}
=1/3
$