4x^2-30=-9-10x

Solution for 4x^2-30=-9-10x equation:

4x^2-30=-9-10x

We move all terms to the left:

4x^2-30-(-9-10x)=0

We add all the numbers together, and all the variables

4x^2-(-10x-9)-30=0

We get rid of parentheses

4x^2+10x+9-30=0

We add all the numbers together, and all the variables

4x^2+10x-21=0

a = 4; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·4·(-21)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{109}}{2*4}=\frac{-10-2\sqrt{109}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{109}}{2*4}=\frac{-10+2\sqrt{109}}{8}
$